| If this is a puppy, it may be losing its baby teeth and sometimes they will bleed from that. If it is an older dog, it may have bad teeth which might bleed easily with a little chewing (Pekingese are known for oddly placed teeth in that tiny smashed face, and their teeth tend to go bad quicker).
Some dogs just go a little crazy with chew toys and chew until their mouth bleeds. If it was previously chewed on, it could have had rough edges and that would have made it worse.
I would definitely have the vet check out the teeth, and don't give the Nylabone back to the dog until the vet says ok. | 
