Rear bumper bike rack - need advice

DO NOT DO THIS! Though they sell those types of mounts and racks for bumpers, this is a very bad idea. The bumper will not last long and will crack. These bumpers are basically thin sheet metal and flex like a beer can. The constant flex back and forth soon destroys the bumper. What you want to do can be done, but the receiver must be integrated with the frame of the trailer not relying on the bumper for support.

I had a buddy weld on such an arrangement on my old trailer and will be doing the same to my new one in the future.