i have dealt with this many times and have learned some great tricks that may help u, but my first question is:
Is the end of the bolt sticking out enough that you can grab it with a pair of needle nose vise grips? IF so, do this:
use a hand held propane torch and heat up the remainder of the bolt. Get it hot enough. Dont be afraid of heating it up too much, it wont melt. now grab a glass of cold water and once you feel its as hot as its going to be, cool the bolt with the water. by cooling it quickly, you are shocking it and breaking the seal that the rust has created between the threads. it should come out no problem with the vise grips.
This has worked for me numerous times with no trouble at all.
NOW, if there is not enough to grab with your vise grips do this:
Heat it and cool it just like the above instructions, but instead of using vise grips, find a stubby flat head screw driver. if you have a grinder available, very lightly sharpen the end so its sharp and flat. Or better yet use a small chisel, if you have one. now use the sharp end and hold it to one side of the bolt. lightly tap the chisel with a hammer and hit it in the direction as if you want to back it out. Once you deform the tip of the bolt slightly, this will provide a "seat" for the chisel to sit in every time you tap it. you will walk your chisel around with the bolt as it starts to move. I hope this makes sense. if not im sorry.
I deal with broken bolts all the time and the chisel method works great only if the seal of rust between the threads is broken.
Good luck.