Evie, offering a bottle is a slippery slope, if you allow her to nurse, your supply will increase. If you keep supplementing with a bottle, it will hurt your supply and your body won't produce what your little one needs. Our breasts are amazing things and adjust very quickly to the new demands put on them.
If I were you, I'd steer clear of the bottles and offer breast instead. Breasts are never empty and although she may not be getting much the first day or two, the nursing will stimulate more milk to meet her demands.
A lot of moms worry that their supply is not enough, but trust me, this rarely happens. And I mean rarely. But all moms worry at some point. Trust your body is doing what it should.
I would suggest going to a 2 hour feeding routine. Does she always fall asleep on the breast because she may not be getting the necessary hind milk for good weight gain. Also, can you hear her swallowing during the 40 minute feeds? She could be using you to pacify, so listen carefully to make sure she's nursing proper through the whole feed.
You could also try breast compressions and that may help her get more of the hind milk and keep her actively sucking.
I hope this helps you a bit.
Good luck.
BTW, how did you make out at the osteo?