You can get a set of left twist drill bits. I have drilled many a bolt with normal high speed drill bits. Your challange is to drill down the middle of bolt and not wander into the threads. I would suggest starting with a small drill bit and work up in size, the larger the hole the easier it will be to EZ out the broken bolt.
Well, I removed the injectors on my bike, and since Ducati chose to use this white goop to seal the threads, and the head of the screws were weak, I had a hell of a time getting one of them out. The head snapped off, and if it wasn't for the fact that I was able to get the other screw out and remove the injector, I would have been in big trouble. All I'm saying is that things can go bad really fast when trying to fix these kinds of problems.+1
The lefthand drillbits work great!
Come on guy's this is such an easy job, you are making it out to be some kind of rocket science...