IMHO $200 and a bike rack on a trailer is not going to pan out. First, few bike racks are rated for TT use, those that are cost much more than $200 and are much beefier than the typical bike rack.
Now that said on our trailer I cut off the factory " bumper" and fabricated a new bumper welded to the frame with a 2" reciever welded on. We use the hollywood rack RV rider on the trailer (even though hollywood racks says 5th wheel only)
Expect to pay in the $400-600 range for a good rack AND add in $$ for making sure the attachment is adequate.
Every bike rack I've seen rated for TT use warns NOT to use a bolt on reciever like the OP posted.