Is it possible for low barometric pressure to cause a nose bleed?

Yes: Rapid drop in barometric pressure is associated with a slightly higher incidence of nosebleeds, although the more important factor is the dryness of the air. Low relative humidity definitely increases the chances of having a nosebleed. The first things to try in cases of recurring nosebleeds involve moisturizing the nose: saline nasal spray, moisturizing nasal gel, a humidifier, etc.