I had to replace a jacked up right shifter recently, and I wrapped the old bar tape around it, and I must've followed the original wrap pattern fairly closely, because it looks pretty good. BTW, this had some adhesive on the back, too.
So, I vote for re-using it, if at all possible. If you get another year or three out of it, then it's money in the bank. Worse case, it looks like crap so you yank it and put on some new stuff. No biggie.