Endos are concerned about keeping tsh too suppressed in women in terms of bone loss---there are studies which my endo and another endo explained to me that after menopause a suppressed TSH can cause bone loss (studies in thyroid in general are pretty small, so who knows).
In my experience, I am not post menopausal, but with my suppressed TSH (kept that way on purpose for thyroid cancer recurrence prevention), I've had bone loss---it could be from something else (ie, genetics), but it could be from my suppressed, as I'm not hyper otherwise.
My Endo (who I respect and like, and has taken good care of me) says it's a balancing act, but I'm betting your doctor might have that concern as your tsh is very suppressed.
Every doctor is different, I'm sure you'll find the right one for you.