If it is a plain steel bumper, them it can be sandblasted. You do not have to be careful of it because the metal is thick enough that nothing will warp it - unlike sheetmetal. I would make sure that it is not a chrome bumper than has been painted over (don't laugh, it HAS happened) by scraping off some paint down to bare metal.
Powder coating is probably your best option for paint. It is the most resiliant for the price, you will have trouble chipping it with even a hammer.
If you are going to go to the trouble of doing this to you bumper, I suggest that you do it to all of your front trim (unless it is chrome). It will all look the same (same paint shade) and is tough as nails. You will probably get a break on price with the powdercoater too - He would rather do a lot of stuff than one or two pieces because it takes a long time to set up his equipment for different colors. You are wasting his time if you are doing only one piece.