There is no specific doctor to treat osteoporosis. The best I can offer is to read this link and consider the suggestions there.
http://www.webmd.com/osteoporosis/osteoporosis-specialist
Thank you for the post, this is what I suspected and I just wanted to make sure. What kind of doctor would you have treat this bone loss?
The doctor is giving you the standard excuse when uncomfortable with actually treating hypo patients adequately to relieve symptoms. Since such clinical treatment frequently results in suppressed TSH, and a Free T3 that is in the upper part of its range, the doctor blames the wrong things. I think you can get some better insight from this letter written by a good thyroid doctor for patients that he sometimes consults with from a distance after initial personal evaluation. The letter is then sent to the participating PCP to help guide treatment. Specially note the discussion about causes of bone loss.
http://hormonerestoration.com/files/ThyroidPMD.pdf
I would push the doctor to test all the possible causes of bone loss and identify which areas are deficient.