The team was paid $10K in 1987 for hosting the on location ballpark scenes. The film was released on this very weekend in 1988, and the Durham Bulls were immortalized. (More on Sunday's game commemorating the movie.)
I discovered an oral history of the film in the wral.com archives. In 2008, for the 20th anniversary, 99.9 The Fan interviewed Kevin Costner, Robert Wuhl, the writer, the producer and others. Slip on your headphones and click here.