For any kind of tape other than cotton (I don't like cork, but I do like Microtek Fizik), I actually use cotton bar tape for top finishing. I do one or two wraps of it, and tack the end in place with some glue. I make sure the end is on the underside, where it's not seen:

(No, that's not an American flag sticking out of my handlebars, it's in the background-- this was on Patriot's day, just an hour before the Marathon bombings, and I had ridden out to Lexington/Concord to see the battle re-enactments).