Why does my nose bleed while cycling and how do i prevent it?

First of all, you should see your doctor. After a checkup he will be able to tell you what is going on. There are otherwise healthy people who have this problem too. Unprovoked nose bleeding is caused by small capillaries hemorrhage in your nose. The strength of your blood vessels both, small and big depends largely on your food intake. You have to take enough Vitamin C and bioflavonoids, copper and magnesium to have strong artery walls. They should be obtained mostly from a healthy diet. Also in your case taking supplements would be wise.