I have always used hairspray on my hand grips. Never had a problem with it yet.
As fr your situation though, I think it is all going to be in the prep work. Take your current grip off. Clean the bar end as thoughly as possible. Essentially, you want to remove all traces of the old glue(s). Next, take a piece fine grit sand paper and scuff up the bar a bit. ONce again, clean it off (To make sure all the dust is off after sanding). As far as the grip goes, your best bet is getting a new one. You can go through the same process with the grip you did with the bar, but it's kind of a pain to do. Basically, you want to get rid of all the old glue completely before you put it back on.
As for the hair spray; spray down the end of the bar (all around), and spray into the grip. Slide it right on and let sit for about five minutes. Clean up any dripping spray and you are all set.