Wish I'd got you instead of the numbskull kid that worked on my bike at the dealer last time. I replaced several fasteners - and, oh yeah, my heated grips - after he was done butchering it.I would NOT try to drill it out, you are just looking to make an inconvenience into a real problem. Try the Torx bit first. If that doesn't work there are some special low priced sockets just made to remove this sort of screw. You can find these at your local hardware store, Home Depot, Lowes, etc. Also there are lots of them listed on Amazon.
Another way is to use a center punch or a small sharp chisel and use it to break the screw loose. you just put the punch to one side, slant it in the direction you want to turn the screw and give it a few careful wacks.
I am a professional with decades of experience. I have removed more stripped screws than I would ever want to count. (Customers screwed them up and then brought them to the shop when they were hopelessly ruined! Gave me lots of practice).
Drilling is a lost resort. Its too easy to get the drill crooked in the hole and make it worse. Then you get an "easyout" down in the hole and break it off only to learn the "easyout" is made of a steel that is harder then your drill bit so your drill goes off center and crazy and then you have a real mess. I can drill a bolt clean in the center, done it many times. But....I learned this in Germany from a Master Mechanic who made you do it over and over until you could get it perfect. It takes a LOT of practice to be good at it. Even so, I find drilling to be the least desireable approach as its just too easy to screw it up.
Next time use a professional grade tool and make certain that is all the way down in the hole and is perfectly "square" with the opening. If the screw is hard to turn give it a few taps with a small hammer to break it loose.