Stop the finger!
Preventing "digital trauma" (or nose-picking) is the best way to head off nose-bleeds.
But if one starts, sit child up, tip head back (placing the nose at the highest point of body so blood drains away from it), & gently but firmly pinch the soft part of the child's nose just below the nasal bone. Be patient! hold pressure for 20 minutes without stopping. A cold compress over the nasal bone helps.