Her first role was as Mary Crow Dog in the television production Lakota Woman: Siege at Wounded Knee, which depicted the 1970s standoff between police and Native Americans at Wounded Knee, South Dakota. She attended The University of the Arts in Philadelphia, Pennsylvania, where she studied musical theatre. In 2005, she was cast in the television miniseries Into the West, portraying the half-Lakota, half-white adult Margaret "Light Shines" Wheeler.
For Disney, she provided the speaking voice of the titular character in the 1995 animated film Pocahontas and its direct-to-video sequel and reprised her role in Ralph Breaks the Internet. Bedard was also the physical model for the character. She appeared in a different take of the story in the 2005 film The New World as Pocahontas' mother. She also played Nakooma in Squanto: A Warrior's Tale, and voiced Carol in the Pepper Ann episode "Dances with Ignorance" and Forest Ranger Hero in Higglytown Heroes.