What kind of doctors specialize in bones?

There are several sciences that deal with bones: Biology, Paleontology, anatomy, physiology, and more.

If you're looking for JUST the study of bones, that would be osteology - although I am not positive that there is truly such a thing. You find references to osteopathy, which is a study of bone disease and disorders. But "the study of" something is an "ology", and the accepted scientific root Word for bone is "oste" or "osteo".