What is a good method to cure dry nostrils causing epistaxis, also known as nosebleeds?

Ointment & saline: Keep nose moisturized with antibiotic ointment or Vaseline; place pea sized amount pressed with pad of thumb into each nostril twice daily. You can also use saline gel/sprays, and use a humidifier at home. Nosebleeds improve with these measures while avoiding picking or scratching in the nose. Consider seeing ENT if you do not improve.

Saline gel: Saline nasal gel, there are several brands but generic is just fine, is probably the best, and most natural way to stop nosebleeds. Apply a small amount to each nostril at bedtime for a few nights in a row, then several nights a week to maintain. You should have much less trouble after that.