Bradley was optioned to Triple-A Durham by the Rays on Thursday, Neil Solondz of the Rays Radio Network reports.
Bradley pitched well in his major-league debut Wednesday versus the Red Sox, getting charged with three runs over five innings while striking out eight. It had seemed like he would be given at least one more start while Zach Eflin (back) continues to recover, but now he can't be recalled for 10 days, unless he's replacing an injured player.