There are those who adamantly say not to add a bicycle carrier to the bumper without some form of reinforcement from the frame of the camper.
I may have just been lucky, but I carried a Schwinn Bicycle for 2 on the bumper of 2 different trailers for 11 years and never experienced bumper failure. The below photo of is from our first travel trailer. Our second trailer was a Keystone Springdale. I don't have any good photos of the carrier on it.
We only carried the one bicycle, and the carrier itself weighs about 50 pounds. It's not light at all. So all together, we had a good 100 pounds hanging on the bumper. But we never experience any failure at all.
Do I recommend it to you? No! Only so I won't be sued for giving you bad advise if I said "Yes" and your's ended up being the one in a million that failed.
My current camper (Keystone Outback) came with a factory installed hitch, from the frame which included the bumper too. I removed the spare tire holder and use it to carry my 3 wheeled tricycle now!
Current trailer (but it has the factory hitch, but I still use the actual bumper as support for part of this contraption.