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...I use a heat gun on stuff like that. I don't think my wife's hair dryer gets hot enough to soften the adhesive, which is what you need to accomplish.
There will be some adhesive residue left after you peel it off. I use mineral spirits on that, first. But if the mineral spirits doesn't remove the residue, I escalate to acetone.

Be very careful with the acetone. It will soften and remove some paints, but not usually the stuff that's used on bicycles nowadays. It's what's in nail polish remover. Don't drip any of it on plastic or rubber parts.