I would try our homeopathic PROMAXOL; it contains a remedy that helps with bleeding and is also used with arthritis. It would also be good to visit your veterinarian to make sure there isn't a foreign body in the nose. If that is clear than having baseline blood work is advisable. If the liver is congested it makes it more likely to have nose bleeds occur. There could be a respiratory infection. If the nose gets dry, using a humidifier to moisten the air is helpful. Giving Omega 3,6,9 orally on the food can help moisten the body from the inside.
Please let us know what you find out and we can offer more suggestions.