I think he's been working hard on keeping his hands inside the baseball on inside pitches.
Against Cliff Lee in his 2nd AB, Lee tried to pound him in on a fastball (first or second pitch, I believe), and he got inside of it and drove a line drive to dead center for a sac fly. Then Pedro Strop, yesterday, had 2 strikes on Bradley, buried a couple off speed pitches that Bradley was able to lay off, and then tried to get in on him. Bradley shortened his swing, stayed in side, and hit a hard ground ball up the middle for a 2 RBI single.
The thing about this kid that makes him so special is that he is able to adapt extremely quickly. He's still going to be vulnerable to the slider away from LHP, which is a filthy pitch to any LHH, but you're going to see him K on those. But overall, he's a very selective hitter who learns quickly and has elite plate discipline.
That's my read on him, anyway.