Check the strength of any bumper on a trailer. They are generally meant to store a stinky slinky or a place to sit, not really strong enough for the torquing motions of a bike rack. Over the years I've seen trailer bumpers, with bikes and rack still attached, on the side of the highway.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI