Go out and get yourself a Mothers California Gold Clay Bar kit. Use this on your bumper and then polish with a buffer. After this is done, put a few good coats of wax or polymer on there. If this doesn't work. Paint Estimates.
EDIT: I forgot to add...the Claybar kit costs around 15 bucks at Advanced Auto. I nice buufer can run you about 100 bucks (I'd recomend a PorterCable 7424). 3M makes some awesome poilishes (I have personally used 3m Perfect it II and have had good results). The wax is up to you . Mothers is always an excellent choice, so is Zaino if you want to shell out 150 bucks for their kit.
If all of this is out of you budget, take it to a detail shop in town and let them hack away at it for 100 or so bucks.