There can be several reasons for bleeding gums or teeth; one can be due to over chewing of bones. It is not unusual for the dog who over chews his bones to have occasional bleeding.  It can be caused due to poor dental hygiene where dog owner fails to brush their pup's teeth regularly, and thus, the pieces of previously eaten bone might have remained stuck in the gums.  The stuck bones slash through the veins and arteries of the mouth, which leads to bleeding in the gums or tooth, and the same shows up on his bone when he chews it.  It is recommended to consult a vet in case the presence of blood on your pup's chew bone gets frequent since it can be something serious as well.