I used to get bloody noses a lot when I was a teenager, especially during dry months in the winter. My mom read in a natural remedies book she had that a boost in Vitamin C can help. I started chewing vitamin C tablets and sure enough my nose bleeds went away. You could also try a humidifier. Bloody noses (especially in the winter) are not uncommon at all, so try not to worry ;-)
Before going to bed every night, carefully place a small amount of petroleum jelly around the inside of each nostril and see if that helps your nose bleeding which may be due to dryness.