The very first thing to do in any abnormal circumstance or accident is to stay calm.
Nose bleeds are actually common to children. Probably because it is them that frequently bumps their noses, or they are the ones with uncontrolled nose-picking. Sometimes there is no apparent reason, and so points to the fragility of the blood vessels in their noses. Since most of their bodily components are yet to develop.
What you should do in a nose bleed case is to pinch the child’s nostrils firmly for about 10 minutes. Do not tilt the head so the blood will not travel down to her throat. Try to stop her from sniffing or swallowing, instead encourage her to spit it out if there’s any in her oral cavity.
If it is still bleeding after the said time allowance, put an ice bag wrapped in a cloth over her nose or a cloth wrung out of cold water if none available for two minutes.
Avoid letting her blow her nose for about 4 hours after the bleeding have stopped. Calling your doctor is necessary if this occurrence becomes constant.