I actually think that Bulger is/was far more suited to running a Philly-style West Coast style offense than he was to running Martz's offense or even the much more conservative Linehan approach that he had a ton of success with in 2006.
I'm betting that if he's put in that system and given an offensive line that isn't utterly putrid, that he's got a chance at a career resurrection. I've got two big reservations, though.
1) Bulger's not that bright about new systems. Linehan had to adapt everything in 2006 to call the plays in the same style that Martz did, using numbers to describe routes, because Bulger apparently just didn't grasp things well enough to keep things straight otherwise. I'm not saying he's terribly stupid, but there's likely to be some growing pains there.
2) Bulger's accuracy went away the last two years.
Rams fans are very fond right now (some of them, anyway) of pointing out Warner's resurgence and saying the same thing could happen with Bulger.
Thing is, with Warner, the passing never went away. He put up one (partial) bad season throwing the ball in 2002, still completed 65.5% of his passes, and then had passer ratings in the mid-80s in '04, '05 and '06. Without the hand and the fumbles, he wasn't throwing the ball badly. And his completion percentage, barring the abortive '03 year that he barely played, was always quite good.
Bulger, on the other hand, has put up passer ratings as bad as Warner's in '02 twice now, and his completion percentage has dropped like a rock. At his best, Bulger was very nearly as accurate as Warner at his best, but now, he's just not throwing nearly as well as you need to.
Maybe he gets it back. Maybe he's just got the yips from the offensive line being terrible, and he'll rebound quickly. I dunno. But I put the odds of his really coming back somewhere around 40%