Does flying cause nose bleeds?

It can: Due to pressure changes in the capillaries in the nasal membranes.

No: Most nosebleeds are caused by injury to superficial blood vessels in the front part of the nose. Anything that causes irritation and inflammation in the front part of the nose can lead to bleeding. Aggressive nose blowing, nose picking, dryness of the air and rubbing the nose can do it. High blood pressure and stress can make it worse as can using Aspirin or other anti-inflammatories.

Depends: In altitudes of 10,000 feet or less not generally. However in higher altitudes without the controls in place, maybe yes. You are reporting from an Air Force Base, so you should review this with your flight surgeon for your particular situation.