One of the most decorated athletes in MU annals, Bradley lettered in football at MU from 1977–81, and in baseball in 1979-80-81. Bradley quarterbacked the Tigers to three bowl games. He was a three-time Big Eight Conference "Offensive Player of the Year" and set the conference total offense record at 6,459 yards which stood for 10 years. In baseball, he starred as an outfielder on MU teams that won the Big Eight championship in 1980, and went to the NCAA Tournament in 1980 and '81.
He was drafted by the Seattle Mariners in the third round of the 1981 amateur draft and made his Major League debut on September 2, 1983, as a pinch hitter against the New York Yankees.
Bradley hit a respectable .264 in his only season with the Phillies. While with Philly, Bradley was hit by a pitch 16 times during the season which set a Phillies team record. Almost one year to the day since arriving from the Mariners, the Phillies, desperately in need of pitching help, dealt Bradley to the Baltimore Orioles for Gordon Dillard and Ken Howell.
Back in the more familiar American League, Bradley's batting average rose to .277 in his first season in Baltimore. In mid-season 1990, he was traded to the Chicago White Sox for Ron Kittle. His final major league appearance came on September 29, 1990, as he drew two walks and scored a run in a 5-2 White Sox win over the Seattle Mariners.
Shortly after retirement, he was hired as the baseball coach at Westminster College in Fulton, Missouri. He also taught classes there, including upper level classes on sports history.