Brian,
Use a piece of 1/8 inch thick steel about 3/4 inch square. Drill a hole in this smaller than the diameter of the broken bolt. Center the hole over the end of the broken bolt and weld it to the bolt inside the hole. You can now weld on a larger diameter bolt. Allow it to cool completely before trying to unscrew the bolt. This method is much easier than trying to weld a smaller diameter bolt to the broken one and the two heating and cooling cycles will help loosen the bolt. I have used this method, without fail, on many occasions to remove broken bolts, studs and dowels. Hope it works for you, please let me know.
Dave