that sucks. I have broken several bolts but not any on the bike. What works for me does not work for some people but you can give it a try if you have the tools that I usually use to do it.
A dremmel to grind the broken bolt surface as smooth as possible
center punch get a dent in to start a drill bit
retract kit choose the drill bit and retract tool that fits (about half the size of the broken bolt). drill about 1/8 deep or slightly deeper if possible and use the retract to reverse drill it out.
to warm up the bike before doing it i dont know if it will help or not. sometimes it does and other times it dont but for sure wd40 it and let it soak a little around the edges
Not sure how much the retract kit cost these days, i have had mine for over 10 years and broken a few during some attempts but it works for me. I need to go get a new set myself. best of luck hope it works for you or some one else has a better or easier way to do it.
