I am a proponent of adding bumper hitches to TT responsibly. Please take into account the load you are putting on the bumper, any additional load-bearing brackets that you may add, and watch carefully for problems anytime you tow. I took off the factory mounted spare tire and bracket. I also have this mounted close to the right side closer to the bumper support.
I added to my Shamrock 183 brackets to help support the bumper (and help compensate for rotational torque from the bike carrier) from
Mount-n-Lock™ Camper & RV Bumpers, Cargo Carrier Trays and Accessories
to give me a little more strength. I added the Swagman hitch from etrailer.com which features a bolt on the side to help control bounce of the inserted hitch.
I then designed and with the help of a friend that could weld aluminum, built a custom bike rack out of aluminum and stainless. It weighs less then 20#. The stainless tube is inserted into the hitch. The tube is bolted to an aluminum rack that supports the wheels of my bike. It is very stable riding down the road and does not bounce by itself, unless the whole rear of the trailer bounces. My bike and carrier weighs about 45# total.
The attached pictures I just took... the uneven black paint near the welds is the result of spray painting black-rubberized paint in those areas to keep ahead of rust, although in one shot it looks like the weld is cracking... it is NOT...
This was my way of dealing with adding a bike rack to my HTT, and I hope it gives you an idea of what might work for you.