He played for the New York Yankees, Chicago White Sox, Seattle Mariners, and Cincinnati Reds.

[2] Bradley was a two-time All-American for the North Carolina Tar Heels[3] and the Atlantic Coast Conference player of the year in 1980.

[5] On February 13, 1986, the Yankees traded Bradley, along with Neil Allen, Glenn Braxton, and cash to the Chicago White Sox for Ron Hassey, Matt Winters, Chris Alvarez, and Eric Schmidt.

The White Sox traded Bradley to the Seattle Mariners on June 26, 1986 for a player to be named later.

He finished the 1986 season strong, as his average increased to .302, having hit 5 home runs and 28 RBIs.

[9] In 1990, Bradley hit .223 with one home run and 28 RBIs, and was the catcher for Randy Johnson's no-hitter on June 2.

[12] In 1992 he pinch hit in the first two Mariners games of the season, earning a walk and striking out, before being released on April 9.

[14] After retiring, Bradley coached in the minor leagues for several seasons, beginning with the Rockies' Double-A New Haven Ravens in 1994.

[11][15] In 1997, he moved to college baseball, coaching for one season an assistant to Fred Hill at Rutgers.

He also coached the general managers of both teams in the 2023 World Series, Chris Young of the Texas Rangers and Mike Hazen of the Arizona Diamondbacks.

[20] The following is a table of Bradley's yearly records as an NCAA Division I head baseball coach.

[27] After college, Kevin signed with the Cleveland Indians, playing in 21 minor league games in 2016 and 2017 before retiring in July 2017.