Bostwick is an expert in Jeet-Kune-Do and Wing-Chun Kung-Fu. His father was a well-known doctor in Montgomery, Alabama.
Bostwick was fired from "Shazam!" (1974) after two episodes into the second season and replaced by John Davey. Bostwick had failed to show up for one day's shooting and the producers accused him of holding out for a higher salary. In truth, Bostwick had sustained an injury during the previous day's shooting and was getting medical treatment. He successfully filed a lawsuit against Filmation Enterprises, who was forced to pay him for the remainder of his contract, including the remainder of the second season.
In the early 1990's, Bostwick's father fell ill, so Bostwick returned to Montgomery. During that time, he taught theater at Auburn University at Montgomery. He also directed several plays, including Ballad of the Sad Cafe, and founded the L.A. (Lower Alabama) Film Group.
Bostwick met his wife, Elizabeth, in Las Vegas, where she was a performer at the time.