Pitching in the highly regarded Arizona State University program, Bannister was The Sporting News College Player of the Year for 1976. Drafted first overall that same year by Houston, the lefty would start for the big club the next two seasons. Plagued with various minor injuries, the Astros dealt him to Seattle prior to the 1979 season.

Though he once lead the AL in strikeouts in 1982 (206), the same year he was selected for the All-Star Game, he never posted an ERA lower than 3.35.

His best season was 1983 with the White Sox, where he went 13-1 after the All-Star break, helping them reach the post-season that year. He soon reverted to his inconsistent form, however.

He later started two seasons for the Royals (1988-89), then served in the Angels' and Rangers' bullpens. He retired after his 1992 season in Arlington.