Servus!
Cool! A Schwinn LeTour! I ended up with the Traveler, a model below it. Served me for two years and about 4000 miles. Mine was this evil baby blue that went with nothing.
I would spray a clear coat from a can onto the bars before I put on the tape. This is what I always did and it kept the crap from destroying the bars underneath. Your mileage may vary...
Mike will probably tell me I was insane. I still use hair spray to atatch the grips to my mountain bike.