I wouldn't have any qualms about adding something to hold a bicycle to that rectangular sewer hose bumper. Mine was really strong on my last RV. I backed up into cement barriers a couple times with no damage. One time I backed into a post and bent the bumper around 2" towards the back of the RV. A few months later, had a friend strap it with a nylon strap, attach the strap to his car and pulled the ripple right out of it. And all that time, I used it to stand on to reach the ladder, or work on the back of the RV.
Here's what I use now, I like the style where the bike hangs from the arms. I'm pretty sure any welding shop would be able to come up with a way to mount it to your bumper:
Curt Bike Rack