DO NOT use the rear bumper to hold a bike rack.
From what I understand, unless bolstered, the bumper has a 75 lb. weight limit and is only designed for the spare. (the spare tire mount is rigid and close to the back of the trailer, reducing vibration).
The rear of any TT (especially shorter ones) will have the greatest amount of oscillation than anywhere on your towed setup and further magnified when going over bumps and thru potholes. Throw in the flexing of the bumper and the rack itself and it's a recipe for disaster.
Bottom line, spend the $$$ and weld a hitch receptacle to the frame. Search for bike racks on Amazon and you'll see that more than half state that they are not RV approved. Here's a quick article on recommendations.
https://www.etrailer.com/question-295037.html
After installation of the hitch, purchase a pair of stabilizers for added safety.
https://www.amazon.com/gp/product/B0...E7U53NWQ&psc=1
An entirely different topic, but load distribution is extremely important in towing safely. After having the hitch installed, I also relocated the spare under the tongue with a winch adding to the tongue weight.
Hope this helps.