Bradley has been added to the Rays' taxi squad and is in line to start Tuesday in Cincinnati, Marc Topkin of the Tampa Bay Times reports.
Bradley was optioned to Triple-A Durham a day after making his major-league debut last Wednesday, but he's now positioned for a long-term stay in the Rays' rotation with Jeffrey Springs (elbow) likely to miss at least the next two months. Bradley struck out eight in his debut versus the Red Sox, getting charged with three runs over five innings along the way. He should be scooped back up in fantasy leagues where he was dropped.