I moved my spare tire to underneath my fiver so I could put a bumper mounted bike rack like the one in that camping world catalog #49401. Mine is a Swagman model but I could not find the part number for it. For the pin to put the rack on it is threaded allowing the bike rack to not bounce at all. I usually carrier a road bike and a hybrid and they have no bounce at all. They also have an optional locking cable that connects to the hitch pin to lock the bikes down and reduce the potential for theft. I really like the rack and would highly recommend it.
Found the Swagman Part #64663. I got mine from etrailer.com. http://www.etrailer.com/RV-and-Motorhome-Bike-Racks/Swagman/S64663.html
I love it and it is truly a very stable bike rack.