Born and raised in Muskogee, Oklahoma, Bradley played baseball and football at Muskogee High School and Broken Arrow Senior High School. In his senior season, he pitched Broken Arrow to a state championship, and was named All-State Player of the Year by The Oklahoman. The Diamondbacks selected Bradley out of high school seventh overall in the 2011 MLB Draft, and he began his first full professional season with the Class A South Bend Silver Hawks. Bradley continued to rise through the Diamondbacks' farm system in 2013 and 2014, but general manager Kevin Towers resisted a push from Bradley's agent to send the pitcher to MLB early, arguing that it would be too much pressure on the young pitcher to ask him to help the Diamondbacks' starting rotation.
