According to here:
The film's name is based on the nickname for Durham, North Carolina, which has been called "Bull Durham" since the 1800s, when W. T. Blackwell and Company named its product "Bull" Durham tobacco, which soon became a well-known trademark. In 1898, James B. Duke purchased the company and renamed it the American Tobacco Company. By this time, the nickname Bull Durham had already stuck.
The film's writer and director, Ron Shelton, played minor league baseball for five years after graduating from Westmont College in Santa Barbara, California. Initially playing second base for the Baltimore Orioles' farm system, he moved from the Appalachian League to California and then Texas before finally playing AAA baseball for the Rochester Red Wings in the International League. Shelton quit when he realized he would never become a major league player. "I was 25. In baseball, you feel 60 if you're not in the big leagues. I didn't want to become a Crash Davis", he said.
He returned to school and earned a Master of Fine Arts in sculpture at the University of Arizona before moving to Los Angeles to join the city's art scene. However, he felt more kinship in telling stories than in creating performance art. His break into filmmaking came with scriptwriting credits on the films Under Fire and The Best of Times .