It's late Middle English bone fire, i.e., a fire with bones used as fuel.
It is said the word bonfire derives from 'bone-fire', and comes from a time when the bodies of witches, heretics and other misfits were burned instead of being buried in holy ground.
Another suggestion is that bone fires' actually refers to the burning of meat bones after feasts. The bones were thrown on fires and the ashes were then spread on the land.