Re: BOLT head in the Bilge...
The good news is that you found the head and it was in the bilge. I once found a 3/8 washer on my deck while sailing off the coast of Baja California. Heads popping off on steel bolts is usually not due to direct stress, but due to hydrogen embrittlement (a manufacturing/processing defect). Other bolts that may have come from the same lot should be considered suspect.
I have made this type of repair several times, and it is unlikely that you can back out the bolt with vice grips, but its worth a try if you can do it while leaving a good bit of the broken bolt protruding. In any case you will need to remove the bracket first. In drilling for a screw extractor (easy out), the hard part is drilling a hole in the broken bolt without running it out into the surrounding part. I would make two drill bushings. Each of these would be a short piece of steel rod with a shallow hole in one end that would fit over the broken bolt extension (there needs to be an extension left) and the first would also have a hole the rest of the way through that would be a close fit for a center drill. This would be used to drill a center into the broken bolt. The second drill bushing would be the same but with the through hole the size to guide the drill for the easy out and used to drill an appropriate sized hole deep into the broken bolt. If you end up just drilling out the broken bolt, it is extremely important to keep the hole as centered over the original bolt as best possible. Good luck