One more tip on drilling out SS bolts. As Dale mentioned above SS cold work hardens. This means if you hit it with a hammer, bend it, drill it, etc it hardens immediately. SS is a soft metal other wise.
On drilling. First off think about what I just said about the metal. This is why you have to use a hard drill bit such as Cobalt and use a LOT of pressure and a low RPM. You want that bit going through the metal before it hardens ahead of the tool (bit).
As far as the drill bit goes I do not use a small bit first. I use a large bit first! Use a center punch to get a center on the bolt and use the large bit to get a crater formed into the center of the bolt then use a bit that will get you to the bottom of the bolt or however far you want or need to drill. Less bit breakage.
Broken bolt removal and heat.
Almost all of the time you can remove an exposed corroded bolt by heat. What you are doing with the heat is melting the corrosion. It takes a LOT of heat to do this and you do not have a lot of time to work with the bolt when you remove the heat source. This is where most folks run in to trouble. When the heat source is removed the metal casting around the bolt cools rapidly and the corrosion sets up again. You really only have 15-30 seconds to work until you have to apply heat again. You may only get the bolt to move a fraction of a turn at first. Stop.....and apply heat again then resume.
When applying heat you will have to get the casting around the bolt hot enough, EVERY TIME, to burn the paint off the casting plus more..........!!!!
Remember this next time you remove a corroded bolt and you will eventually get pretty good at it.