I would recommend left-handed bits if you can get them. Ace Hardware carries them, and I have also bought them on eBay.
Do the best you can at centering the bit on the jet, and slowly increase the bit size. The remains of the jet will likely unscrew when the bit is big enough. If you find you're beginning to nick the threads in the bowl, it's time to put down the drill and pick out the remains with an awl or a similar sharp-pointed tool.
Mark W. in MI