Humidify air. Babies can develop nosebleeds if the delicate skin inside their nose cracks and dries out or through mechanical trauma such as nasal suction or nose picking. Moisturizing the air with a humidifier and placing vaseline in nose with q-tip prior to bedtime can minimize bleeding episodes. If the nose begins to bleed pinch the nostrils continuously shut for 5 minutes.
Nosebleeds. A common additional cause is nose-picking at night so make sure the child's nails are closely trimmed. Some children have to wear mittens at night to allow their nasal scabs to finally heal.
Moisture. Epistaxis is common in everyone. 80% of people experience this in their lives. A common cause is dry, hot air like inside the home in the winter causing nasal dryness and crusting. The nasal tissue cracks and bleeds easily. For your baby try, a little vaseline inside the nostil at bed time and try "little noses" saline drops. Use them twice a day. If no help, see pediatrician or ent.
Press on one nostril. Babies generally don't get nosebleeds. If a baby has some blood-stained mucous more than once, during a cold, a parent should talk with the doctor. If there is a real nosebleed where red blood is oozing out, one can press the bleeding nostril (bleeding stops after 5 minutes or less) and talk with the doctor also. One should not press both nostrils together (baby would have trouble breathing).
Some preventive tips. For an active nosebleed, gently pinch your child's nose with a tissue and sit up leaning slightly forward for a few minutes. Prevention may include using a humidifier in the bedroom, use of a small amount of vasoline just inside the nose (apply with q-tip or finger) once or twice daily, and keeping fingernails trimmed since nose picking is one of the most common causes.
Put down the sucker. Most nasal bleeding in infants is caused by too much nasal suction! first, use saline nose drops every 3-4 hrs for a few days. Run a vaporizer at night and put a small amount of vaseline around the baby's nostrils every night. Don't suction unless the nose is so blocked that it's bothering him more than you!