If you mean bow limbs made of bone, like the fictional World of Warcraft "Bone Bows", then I would say no. IMHO bone, as such, is too stiff and brittle. It doesn't bend - it breaks.
Horn, antler, even ivory - in thin plates - is used in making Asian style horn & sinew composite bows. But that is not bone; it has completely different properties, including the flexibility necessary for a bow. Bone itself is seldom used, even in small pieces, in such constructions.