What are possible reasons that I keep getting small nose bleeds?

Nose bleeds. Most commonly, nose bleeds are the result of excessive dryness of the nasal membranes. Sometimes they can occur because of allergies, a deviated septum or a growth in the nose.
Dry nose. The tiny capillaries at the front of the nasal septum can bleed when the lining of the nose gets too dry. This can happen anytime of year, but is often worse with winter heaters, dry central air systems, a fan blowing directly. Also, if the septum is deviated, there can be preferential drying of one side, causing that side to bleed more. Other causes are blood thinners, allergies, & nose picking.