Bullseye is a supporting character in Disney/Pixar's Toy Story series. He is a toy horse that was a part of Al's collection, which had been in storage for several years.
He was the first Woody's Roundup toy that Woody met when he arrived at Al's apartment. Despite the fact that he is a horse, he has traits of a puppy dog. He was extremely affectionate toward Woody, Jessie, and the other toys. He doesn't have a speaking voice; instead, he neighs and makes other horse noises.
In Toy Story 2, he is a toy horse that is part of Al's Roundup collection, which he intends to sell at a toy museum in Japan. He is the first of the toys that Woody meets when he arrives at Al's Penthouse. Being in a storage for several years, Bullseye is excited to see Woody finally join the collection. He is shown to loathe fights, as seen when he hides into a can when Jessie is about to pounce on Woody for blaming her for the TV incident that prevented Woody from getting his severed arm back himself. However, Stinky Pete the Prospector stops the fight, and Bullseye expresses disappointment as much as Jessie does when Woody declares he will leave as soon as his arm is fixed. Later, when Woody is about to leave the apartment after having his arm reattached, Bullseye is still shown to be upset, but later brightens up after Woody, having learned about Jessie's tragic past, decides to stay with the gang to go to the museum.
When Andy's toys, led by a new Buzz Lightyear, break into Al's Penthouse, Slinky and Bullseye have a growling match that Jessie tries to stop, but Slinky coils her up along with Bullseye. After Woody decides to go back to Andy's house, he decides to take the Roundup collection with him. And when he asks Bullseye, the horse eagerly licks Woody. However, Stinky Pete locks Woody, Jessie, and Bullseye inside the room, and the Roundup toys end up being loaded into Al's case for its shipment to Japan from Tri-County International Airport.
At the airport, Bullseye manages to escape the case just before it reaches the end of a conveyor belt, but Jessie still remains trapped inside the case as it is loaded into the luggage transporter. Woody and Buzz mount the newly freed Bullseye, and they gallop across the airfield to rescue Jessie. Despite being separated from Woody, Buzz orders Bullseye to follow him, as they are later seen galloping next to the front tires of the plane when Woody and Jessie climb out of the aircraft. Woody and Jessie swing between the tires through Woody's pull-string, and they land on Bullseye, right behind Buzz, just before the plane takes off. Back at Andy's house, Bullseye (and Jessie) are now part of Andy's toys and has every letter of Andy's name printed on the sole of each of his hooves. Finally, Bullseye joins the other toys as they gather round to see Wheezy sing "You've Got a Friend in Me."
In Toy Story 3, he is first seen in Andy's realistic play scenario when he ferries Woody and Jessie as they chase after a train, which has been robbed by an evil, nefarious bandit couple One-Eyed Bart and Betty (portrayed by the Potato Heads).
Years later, when a teenage Andy opens his toy box to decide what he will do with the toys, he puts Bullseye in the bag destined for the attic. But Andy's slightly-aged mom mistakenly thinks that the bag is trash, and puts it out on the curb. But Bullseye, along with the other toys that have ended up in the bag, manage to escape and board the box bound for Sunnyside Daycare. Bullseye decides to follow Woody back home when Woody decides to leave Sunnyside, but Woody persistently insisted Bullseye to stay with the other toys as he didn't want him to be lonely in the attic, leaving Bullseye heartbroken.
When Woody, having learned of the evil intentions at Sunnyside, returns to the daycare center and reunites with his friends, Bullseye gives Woody his hat back. Bullseye also gives Mr. Potato Head (who has caught up with the toys in a cucumber body after his tortilla body is destroyed by a pigeon) his plastic potato body back when the toys escape Sunnyside.
Finally, Bullseye, along with the other toys, is given to Bonnie Anderson by Andy when he goes away for college. In the end credits, he turns on the boom box to play "Hay Un Amigo En Mi", the Spanish version of "You've Got a Friend in Me" to which Buzz and Jessie perform a pasodoble.
Bullseye appears once more in the fourth movie, though like many of the other toys, he has a very small role in the ultimate story. He first appears in the flashback nine years prior to the third and fourth film. During a thunderstorm, Bullseye covers his eyes as a flash of lightning strikes down. Jessie comforts Bullseye as she looks out the window, saying that she hopes Andy and the gang make it back alright. Hamm then warns the two that Andy's coming. As they all go limb, Andy comes in and dumps the rest of the gang onto his bed to head downstairs for dinner. After he leaves, the toys jump up and begin to panic because Andy accidentally left RC outside in the thunderstorm. Woody, Jessie, and Bullseye look out the window, but can't spot him anywhere. Woody then tells Buzz, Jessie, and Slinky to follow him to Molly's room while the rest of the gang stays put. It can be assumed Bullseye was saddened by Bo Peep's departure after being sold off to another owner. He is later seen throughout the You've Got a Friend in Me sequence, being played with by Bonnie.
Nine years later and two years after the third film, Bullseye now lives with the rest of the toys with Bonnie being their new owner. He first appears with the rest of the toys waiting in the closet for Bonnie to finish her breakfast. The toys are cramped and annoyed with one another, with Bullseye comforting an anxious Jessie as she does her breathing exercises while she sits on him. He, along with many of the other toys, is played with more prominently than Woody, who Bonnie neglects. When Bonnie arrives in her room, she plays "town", and uses Bullseye as Jessie's horse while she leaves Woody in the closet. Woody watches in sadness as Bonnie plays "Hat Shop" and tries Mr. Potato Head's hat on Bullseye. Suddenly, Bonnie's father walks in and tells her to get ready for kindergarten orientation, much to her dismay. When Bonnie asks if she can bring a toy (namely Jessie) with her, Mr. Anderson says toys aren't allowed in school. After they leave, the toys are about to get up when Dolly tells everyone to freeze, since Bonnie always forgets something and could be back any second. After seeing Bonnie crying under her bed when she comes back into the room, Woody decides to sneak into her backpack to keep an eye on her, much to the other toy's dismay. During her orientation, she creates Forky, a spork who suddenly comes to life.
When Bonnie returns and drops her backpack off in her room, Woody climbs out and is scolded by the rest of the gang for breaking the rules. But Woody alleviates the situation by saying that not only did Bonnie have a great day in class and they're all going on a road trip (to which Jessie hugs Bullseye in excitement), but Bonnie made a literal friend in class. Woody pulls out Forky and introduces him to the gang. Like the others, Bullseye is both shocked and confused by both Forky's existence and his love of trash. They then watch in confusion as Woody fishes Forky out of the trash, saying how he'll keep an eye on his during the road trip.
Bullseye is then seen throughout the I Can't Let You Throw Yourself Away sequence, sitting still as Woody frequently keeps Forky from throwing himself out. That night, while everyone else is asleep, Forky escapes out of Bonnie's hands and jumps out of the RV window. Woody then says he'll meet them at the RV park in the morning with Forky and jumps out the RV window.
The next morning, the toys sneak a spoon into a sleeping Bonnie's hand as a substitute for Forky, but to no avail, as Bonnie is distraught over losing her favorite toy. As she goes outside with her parents to look for him, the toys contemplate on what to do. Buzz (after listening to his "inner voice", AKA his voicebox) then states he must go find Woody and Forky and jumps out the window, leaving the other toys to make sure the Andersons don't leave the RV park. Meanwhile, Woody talks to Bo Peep (who is now a lost toy and helps Woody rescue Forky from the Antique Store) mentions to her how the whole gang is still together, including Bullseye.
That afternoon, the gang begins to panic as the Andersons prepare to leave with Buzz, Woody, and Forky still out there. While they struggle to think of a plan, Jessie quickly leaps out of the window and pops the front tire of the RV, much to the group's happiness.
By that night, Mr. Anderson finally fixes the tire, but Buzz arrives just in time. Buzz explains to the gang that he and Woody must be extracted from the Antique Store. As the Andersons climb into the RV, the toys collapse. Buzz whispers to the gang that Bonnie will realize she left her backpack back at the store and they will go back for it. But Bonnie doesn't notice and the RV begins to drive off. Buzz uses his voicebox and his "inner voice" once again to think of a plan. Mrs. Anderson believes Buzz to be broke and throws him in a drawer when Buzz quickly yells out to Bonnie (in a way to sound like one of his phrases): "Your backpack is at the Antique Store. Let's go!" The plan works, and the RV turns around to return to the Antique Store.
After getting her backpack with Forky inside, Woody sneaks off to help Gabby Gabby and tells him to get the RV to the carousel as a meet-up spot. While Bonnie is sleeping, Forky explains it to the gang, and Jessie comes up with a plan. Buzz climbs to the roof and tells Mrs. Potato Head where to go using her ear. Meanwhile, Mrs. Potato Head hides under Mr. Anderson's seat and repeats the directions to Trixie, who mimics the GPS in order to tell Mr. Anderson where to go. When the plan begins to fail, Buttercup then sneaks under the gas pedal and pulls it forward so the RV can go faster, eventually causing the RV to be chased by the police.
After successfully getting to the RV to the carousel, Buzz tells everyone to get to the roof while Forky locks the Andersons out of the car after dealing with the police chasing them. After stacking themselves up, the toys open up the awning as a bridge between them and the carousel. They soon climb up and the older toys are shocked to see their old friend, Bo. Woody, who wants to stay with Bo and help other lost toys, is given a large hug by Jessie. Bullseye then runs up and begins licking Woody's face, which eventually causes the rest of the gang to join the hug. Forky sneaks up to join them but leaves the doors unlocked, causing the RV to pull away. After jumping back into the RV, the gang watches as Bo and Woody wave goodbye on top of the carousel.
A year later, Bonnie drops off her backpack after her first-grade orientation. Jessie emerges from the bag and is barraged with questions by the other toys. Jessie interrupts everyone by saying Bonnie made another new friend and introduces the gang to Karen Beverly, a toy knife Forky becomes smitten over.
Bullseye was originally going to have a speaking voice by Martin Short, but John Lasseter decided to make him a non-speaking character since he thought it would be more appealing to audiences.
During the rescue scene in Toy Story 2, Bullseye is somehow able to run just as fast as a plane getting ready to take off, similar to how RC can catch up to a moving truck in the first film.
Bullseye may have been an inspiration to Sven the reindeer from Frozen in the sense that they both act as dogs, are very cheerful, and show extreme loyalty to their masters (Kristoff and Jessie respectively).
Even though he is Woody's horse, Bullseye seems to be more attached to Jessie, as shown mostly in Toy Story 3. He can be often seen with her at his side, usually with an arm around him. Other times (such as when something dramatic is going on), he can be seen hiding behind her, almost as if it were for protection or out of habit. This is probably due to spending more time with Jessie while still living in Al's apartment, although his loyalty to Woody still remains, such as when Woody tried to get his arm back from Al, or when Woody left Sunnyside Daycare.