He attended Lamar University for two years before, in 1980, transferring to the renowned California Institute of the Arts, where he studied animation and filmmaking. He is known for being an artist in a variety of capacities, on many animated movies.
Outside of Disney, he directed Spirit: Stallion of the Cimarron, Shrek 2, Smurfs: The Lost Village, and Ugly Dolls.
On June 26, 2020, Asbury died of complications of abdominal cancer at the age of 60.
- The Black Cauldron - 1985 - In between Artist
- Sport Goofy in Soccermania - 1987 - Layout artist
- The Little Mermaid - 1989 - Visual Development Artist
- The Rescuers Down Under - 1990 - Character Designer, Storyboard Artist, and Visual Development
- Roller Coaster Rabbit - 1990 - Art director
- Beauty and the Beast - 1991- Story
- The Nightmare Before Christmas - 1993 - Assistant Art Director
- Toy Story - 1995 - Story
- James and the Giant Peach - 1996 - Artistic Supervisor
- Gnomeo & Juliet - 2011 - Director, Story, and Screenplay, voice of Red Goon Gnomes
- Wreck-It Ralph - 2012 - Story artist
- Frozen - 2013 - Additional story artist
- Quack Pack - Storyboard artist