I usually don't do that, the price of a new bumper is less than the labor of stripping, USUALLY!!!!
But I have stripped them, I use paint stripper and have never had a problem with it.
I like the stripper in a spray can so you can keep spraying it on without disturbing it.
You can buy it in a spray can at auto stores like Autozone or you can pour stripper into
a spray bottle made for it. The main thing is making sure you clean it real good after stripping.
I use a scuff pad with Dawn dish soap.
If you want your bumper to stay free of the road rash caused by rocks and such, then
put epoxy primer on your bumper after a good adhesion promoter and it'll reduce the chips 90%.
It makes a huge difference, just make sure your epoxy is a flexible one, if not add some
flex agent like Bulldog and you're good to go.
I paint mostly bumpers and the epoxy has made a huge difference for adhesion.