Get yourself a set of left handed drills and a hinge drill bit set. combine the two to make a left handed self centering drill and use this to drill a little way into the stuck bolt - if you are lucky the bolt will undo when the drill grips.
If this does not work try an 'easy-out', you may get lucky!
Obviously that didn't work, so heat up the bolt till just too hot to touch then squirt a blast of WD40 into the hole in the bolt - you've still got the bit of red tube they give you for squirting WD40 into hot bolts haven't you? now give at it with your left handed self centering drill and the remains of the bolt will unscrew, unless it doesn't in which case it is off to the shop . . .