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I'd try lacquer thinner... in my experience that stuff melts just about any plastic! You might even want to mask the bumper first in case of splashes. Have some clean rags or some wooden sticks/paint stirrers handy to wipe the plastic goo as the lacquer thinner evaporates right quick.
Other chemicals that may work would be PVC pipe cleaner, the clear water-thin stuff (not PVC primer). I believe it's a mix of MEK and acetone. It dissolves PVC, which is probably what that plastic film was made of.
Don't underestimate the ability of the metal polish and buffer to do the job. This is a picture from my water pump DIY showing before and after polishing my muffler...