Marks on your car bumper can ruin an otherwise-perfect paint job. Marks can be anything from road tar and paint to scuff marks. These marks can damage the clear coat on the bumper, but if the damage is not too severe, the bumper can be repaired. You'll need an orbital buffer that can be purchased from most auto parts stores. The orbital buffer will allow you to create the circular friction needed to buff out any marks on your plastic bumper without damaging the bumper.
Apply a liberal amount of polishing compound to your bumper.
Turn the orbital buffer on and work the polish into the bumper. Pay special attention to the marks on your bumper. You don't need to apply any pressure to the buffer; just allow the buffer to do the work. Since this is an orbital buffer, you need to work the buffer only in a linear fashion, moving back and forth across the surface of the bumper.
Wipe down the bumper with a clean, lint-free towel once all of the marks have been worked out of the bumper by the polish.