Via FanGraphs, Bradford's gamelogs:
Don't worry about the hits column, he's playing with weaker defense than the Rays offer. The encouraging, and probably obvious sign is Bradford's K/BB ratio. In recent years, Bradford's K/BB ratio has decayed, mostly due to a sudden decrease in strikeouts. Which doesn't make a ton of sense to me because nothing changed in Bradford's approach.
Also worth noting, Bradford's role in the movie adaptation of Moneyball will be filled by rapper/actor Mos Def.