I've got a bit of experience with this problem on cars, since I live in MA ... and as of late, the state has decided to use a "bare-road" policy when it comes to snowstorms -- read" MEGA salt assault!
Since folks here can't possibly use common sense & drive according to the conditions ... but I digress ...
Many ways to tackle a flush-busted bolt, as was previously mentioned. I used to go the Easy-Out route, but I don't have the patience anymore ... and since I've broken more than my fair share of those off INSIDE the damn bolt that I was supposed to be removing - making drilling them out a slow, painful process - I don't use them anymore .. unless I'm 200% certain whats left of the bolt will come out easy.
The quick and easy route is what Richard suggested -- just hog it out with a drill, one, or 2 sizes bigger & tap the threads & install the bigger bolt. The other option if you want to still use the same size bolt is to drill for a Helicoil, or a Time-Sert. I'm partial to Time-Serts, but they are VERY expensive ... but by that same token, they are VERY strong, and will outlast anything you install it in. I've managed to yank out a few Helicoils accidentally, but have yet to damage a Time-Sert in any way, shape or form. The other option is the EasyOut, but you need to drill DEAD CENTER of the bolt. Not easy without a punch. I've never used a punch .. and I've never had it dead center... which could explain a few of my EasyOut failures ... but anyway, it's another option. Choose what you will.