This site goes over nasal bleeding and includes some first aid like a cold compress over the bridge of the dog's nose
http://marvistavet.com/html/body_epistaxis__the_bloody_nose.html
It also goes through the testing done to figure the problem out.
This could be anything from high blood pressure, a bleeding problem, a tumor, an inhaled weed seed etc.
You can read more about nasal issues here and see a good picture of how complex the nose in a dog is too
http://www.vetmed.wsu.edu/ClientED/nasal.aspx
If this is a nasal cancer I had good luck with treating using Piroxicam and Misoprostol to keep the dog out of pain and shrink the tumor a little and keep the stomach from being impacted by the pain med.
I'd plan on seeing another vet than a pet smart vet.
Hope this helps you!
Dog Expert:Rescue, Train,Breed,Care
30+ yrs dog home vet care & nursing, rescue, behavior&training, responsible show breeding, genetics