Bradley was outrighted to Triple-A Jacksonville on Monday, per the MLB Transactions Log.
Bradley was booted from the 40-man roster Saturday and will now report to Triple-A after failing to draw any interest from around the league. He's tallied a 2.95 ERA and 0.99 WHIP with a 16:5 K:BB across 18.1 frames so far this season for the Jumbo Shrimp.