I would suggest you take that poor dog to the vet immediately, that is dont wait! If he is bleeding and has problems with his snout it could kill him. I cant believe you would wait for some one to email you about this!

At the kennels where i work one of our greyhounds was attacked by a jack russell. The greyhound was badly bitten on the nose and when i took him to the vets they gave me some tablets to stop infection setting in. Also, while i was there he said that clotting may occur due to the wound, which may force blood out through other places. This could be why your dog is bleeding around her eyes. It is not a dangerous clot as it is only around the nose area but if left it may start to irritate the dog and become infected so id take it to the vet as soon as possible.