I'm no help on drill bits, unless you want to know how to break one off inside the stuck bolt. But here is what I do if I have a little room to work.
I try to do is get the face of the offending bolt cleaned up by: Flattening the surface with a demal bit, then with another very small round dremal bit I make a divot and start on a cone shaped cavity. I make is so the bit cannot wander. It's patient dental work, but I have success. I've even used small dremal bits to get a deep enough cavity to get an easy out in. Plus the cavity releases pressure.
Good luck, broken bolts are a bummer.
j