Bystrom was signed by the Philadelphia Phillies as an amateur free agent in December 1976. As a September call-up at age 21, he made his MLB debut on September 7, 1980, winning 5 games (including a complete-game shutout) during September for the Phillies en route to their National League East Division championship.
On June 30, 1984, Bystrom was traded by the Philadelphia Phillies along with Keith Hughes to the New York Yankees for pitcher Shane Rawley.
Following the 1985 season, Bystrom was granted free agency and signed with the New York Yankees. However, he would never again reach the Major Leagues as he finished his career pitching in the farm systems of the Yankees, San Francisco Giants, Phillies, and Cleveland Indians until his professional retirement in 1989. Because of the 1994 MLB players' strike also affected 1995 spring training, he briefly attempted a comeback as a replacement player because "no matter what, there's nothing quite so special as putting on a major-league uniform and playing baseball. I cherish this. I always did."