I just bought some tung Oil, what is the best way to apply it to a bowl? Should I just apply it the way I do Myland friction polish, or should I remove it from the lathe first?

Flood it on and let penetrate, then wipe off excess. You can do it on the lathe, not running, but you will probably get some tung oil on your lathe. Be very careful with any rags or paper towels that get the oil on them. They can create a fire. My MIL almost had her house burn down from some rags soaked with oil finish. She hung them out to dry/cure, but didn't leave them long enough before putting them in the garbage can in the garage. Luckily the dog woke her up before the house burned down. Lots of smoke damage though.

Yeah, what Doug said!

My only experience is with old masters 100% tung oil. It takes it a couple of days to dry if not thinned. I have been thinning it about 25% and waiting at least 24 hrs between coats.
If you are going to buff wait several days.
Gary