Some small scuffs on my bumper from lightly rubbing against parking lot pillar.

Do I just use a rubbing compond and wax and hope for the best or is the bumper different from the rest of the car?

(Car is brillent black and you can see small white sctraches in the bumper, i guess that's primer)

It does a pretty good job of cleaning the paint. That white is probably some residue from the parking lot pillar. Usually, if you scratch the bumper, when the paint comes off you just see black (the color of the plastic bumper). Follow up with a quality wax.

can barely see them now