Made from the bones and teeth of dead humans and animals, bone is a component used to craft various mods and tools. Bone is most useful for crafting cutting fluid at the chemistry station; cutting fluid, in turn, can be scrapped for oil.
A few locations with a decent quantity of respawning pieces are:
Wildwood Cemetery - There are several open mausoleums that the player character can enter and pick up at least 25 bone fragments out of already opened coffins, for a total bone count of at least 65, and they will respawn after some time, just like other standard loot around the Commonwealth.
Rotten landfill - The area spawns a large number of mole rats when first entered. Later visits spawn about four mole rats. Their teeth can be converted to bone. Slightly west from the rotten landfill up the hill is an iron fenced cottage with four skulls on display. Beware of a radscorpion when entering the cottage.
Dunwich Borers - At the bottom of the mining area, bones can be found scattered in the center area underneath the cages. The cages themselves can be opened to find more bones.