To make you feel better. The same thing happenned on my car and the mechanic drilled it out in about 15 mins. If I remember correctly it is drill slowly, with a good quality metal drill and use a lubricant to keep it cool such as oil or fairy liquid , I had bought cheap bosch drill bits in a set and they were rubbish. i thought how can people drill with theseand get metal out so decided to buy a better brand and they just cut through the metal bolt like butter. I would recommend using gloves to prevent the turnings going into your skin.
I also now have a bolt removing kit in the house that i purchased just in case of emergencies.