I used to use double sided tape, glue, single sided tape. Then, one day I tried wrapping it REALLY tight. Viola!, no more glue and no problems with bar wrap. Sometimes re-using wrap can be a little tricky where the downtube bars turn, otherwise no problem.
BTW, I reuse all kinds of bar tape. Cork, gel, latex you name it, if it's still in good shape, I re-use it. If the cork is dried out or if the latex is separating, then it's not worth it.