There's a couple of tools that make bolt extraction a little easier. The first one I would try is a reverse drill bit. A reverse drill bit looks just like a standard drill bit but it drills in a counterclockwise direction instead of clockwise. If you start drilling into the center of the bolt, it will drill partially into the bolt and at some point, the tip of the bit should grab onto the bolt and twist it out since it's going in the same direction you would twist it to loosen the bolt. Sometimes, if the bolt has been torqued down too tight, a reverse drill bit won't work. If that's the case, keep drilling the hole in the center of the bolt with the reverse drill bit until you've gone about 1/4 to 1/2 an inch deep. Then try using an easy out to extract the bolt. An easy out looks kind of like a tapered drill bit. I've shown a picture of one below. (You can buy a kit that has both easy outs and reverse drill bits) Choose the right size easy out for the size of hole you just drilled. The tip of the easy out should go partially into the hole, just enough to grab onto the bolt as you twist it counterclockwise. With the easy out in the hole, put a wrench or socket on the end of it, push down hard and twist counterclockwise. That should hopefully extract the bolt.