I was recently in a minor accident and banged up the front right bumper on my car. I drove away from the accident with not evidence of structural damage to the car, other than a dented bumper. However, I have sense noticed a high pitch squeaky noise coming from my wheels when my car moves, whether I’m using the accelerator or not. It sounds as if it is metal rubbing against metal. I recently had new brakes and tires put on the car, and neither mechanic seemed to notice anything major out of the norm. The car is rusty in the under-carriage area.
Try bouncing the front of the car and/or shake the bumper up and down, and see if you can duplicate this squeaking noise. I'm thinking that you have damaged or partially broken the r.f. bumper bracket, and you have a "metal on metal" squeek caused from the movement of the bumper. The bumper may also be rubbing on the r.f. fender, or the r. f. wheel could even be rubbing on the r.f. fender. It all comes down to how badly it is "dented" and what associated damage occoured, and without a photo it is hard to guess, since dented is a "relative" term. ie: your dented bumper may be worse than my dented bumper. I have seen some dented bumpers that required the replacement of the front fenders and the McPherson strut suspension. ;-)