It has long been debunked that drinking caffeinated beverages, such as coffee, increases risk of dehydration. While diuretic, caffeinated drinks can contribute to your daily fluid requirement and does not cause excess fluid loss.
However, this does not go on to say that caffeinated drinks are without a "dehydrating" effect. Drinking excess amounts of caffeine can pull out moisture from your body, including the mucus membranes in your nasal passage. Without moisture your nasal passages dry up, becoming irritated and inflamed. This increases the likelihood of getting a nosebleed, as injuries as small as picking your nose can cause blood vessels in your nose to be injured.
The bottom line is this: while caffeine does not dehydrate you, drinking too much caffeinated drinks can remove the moisture from your nose, increasing the risk of nosebleeds.