Only do this if you have an obsessive composite disorder, like a perfectionist or something!!!
If the paint did not have a good plasticizer in it the paint will come off with your fresh coat on top of it. I would remove the bumper, strip it with paint stripper, bondo it, seal it with a zinc chromate epoxy primer coat, then prime/paint it using standard practices recommended by the Mfg of the paint. Use a quality plasticizer so the paint will remain flexible!!!
Be sure to post pics!!!!