Heres an easy one I learned over the years. After you get the bumper close to where you want it polished, spray a clear coat on it (the factory bakes one on). The best paint I have found is one of the auto specified type like Duplicolor but I'm sure there are others. The satin works the best if you don't want the glossy look. The bonus is it brings back a more even factory look and is protected for a long time if you wax it. This works great in the engine bay (or anywhere else inside or out the car including wheels) to spray what you just repainted or spray it on existing paint to bring back the deep color and preserve it. This is what Jessy James of motor cycle fame does to the cars in his collection that have original paint worth saving. You can test it by wetting an area with water or WD-40 is even closer to the final look. But you must clean the area really before painting of any grease, grime, WD-40 which is a given.