"Bones is short for "sawbones," an ancient description for a surgeon."
According to Memory Alpha.
No known onscreen reference.
Well, I vaguely recall Kirk did call McCoy "sawbones" once. I think it was in "A Piece of the Action".
--edit: I found the dialogue
MCCOY: Jim.
KIRK: Knock it off, Sawbones. I want to talk to this creep. Now listen, I'm getting tired of playing pattycake with you penny-ante operators.