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You can do it. I did Just sand the bumper and spray an adesion promoter. Then prime it and paint it. Then clear coat it. My bumper has held up for a year so far with no chips. It is a lot of work though and make sure you clean it good and wet sand after each color coat and buff out the clear coat for a glossy finish. It will be cheaper and as long as you prep it right will last forever.
I just scuffed it up real good. You can still kind of see the texture on my bumper. If I did it again I probably sand it more or you could spray more coats to fill in the texture. I hate painting I don't have the patience for all the wet sanding in between color coats and all the buffing but it came out ok and has held up pretty good.