Do not do it!!! As you mentioned and sound concerned with, the bumper is not strong enough at all to support a bike rack.
You have a '15 Jayco? Is there a tab on the bottom of the frame behind the rear scissor jacks on each side? Look in my mods link for the optional Jayco rear cargo receiver hitch we added to our 32. It bolts on to the frame mounted tabs, and is pretty solid.
Even still, make sure you get a good bike rack. Some are rated for use on the rear of a rv. I also use one of the anti-rattle kits to keep our bike rack from moving in the receiver hitch.
Just looked up your model. Didn't realize it was a Whitehawk at first. Jayco unfortunately does not list the optional rear hitch like what we added.
I would suggest finding a local welder and talk to them about adding a frame mounted hitch. They may even just reinforce a bumper mount hitch so it is also tied into the frame. A buddy had that done. The welder made the bumper mount into a "T" that extended toward the front a foot or two, then tied into the frame on each side. No pics and they have a different trailer now.