I just took my 4yr old to the doctor last week because of a nose bleed. Though he does not have them frequently, this one was spontaneous (though his little fingers do travel into the nose) and a bit worse than his last episode. Thankfully his stopped after a few minutes. The doctor did give me some good advice to prevent nose bleeds that I'll share:

Saline spray (we use Little Noses) is great for keeping the nasal passages moist

Nasal gel (Rhinaris is one name) is a moisturizing saline mist...a bit more than just a saline spray.

Vasaline rubbed just inside the nostril can help as well.

Thank you Debbi! Jazz has SUCH aversion to having her ears or nose "messed with" but I do use a saline spray and a bit of neosporin at night as well as a cool mist humidifier to try an alleviate these darn things, but they keep on happening. I wasn't sure if it had anything to do with "being on the spectrum" or totally random. Ill try the Rhinaris since I think that Neosporin is a really bad idea in the nose,so thank you for responding!!

Yep. Go see a ENT. they put something in his nose like a solved cream...never had another one.

Thank you Debbie, I appreciate your advice! Living in the desert, I guess I should have thought of that!

lot of nose bleeds here as well. An iron deficiency may be one reason. Dry climates also can contribute.