I'd go with the others that say steel wool as well, I've got 0000 I use on some stuff, it barely even scuffs paint, it feels about like human hair, if not softer. It's useful to have around for other stuff anyways...polish brass, etc.
No fancy compound is going to do anything more than you can with any appropriate abrasive. The rust means the chrome (actually all three plating materials, copper, nickel and chrome IIRC) has been penetrated to the base metal, the only real fix is to have the piece rechromed. All you do with polish is remove the rust stain from the surrounding chrome, and maybe some sort of protectant coating to make the "fix" look better longer. If you took the actual rusted portion down to clean metal and clear coated the spot, you might get some fairly decent protection against recurrence, but that's a lot of work for minimal gain.
It's cheap to buy a used bumper in good shape (if you can find one) or still likely cheaper than having yours rechromed, go buy one of LMC's premium chrome bumpers.
For a quick fix, steel wool will take the rusted stains off the bumper, up close you'll be able to see the "pinholes" where the rust has stated, but it will likely look quite a bit better for awhile.
