I've had near-daily nosebleeds since I was a toddler. It wasn't until I broke my nose at 18 that I was diagnosed with having a deviated septum (so like my nostrils aren't separated inside my nose, it's just this one big cavity in there-- lovely!). I still get frequent nose bleeds & the one thing that saves me from constant uncomfortable dry nose & bloodiness is Vaseline! Yep, I put that slime up my nose several times every single day (*especially* before I go to bed).
You could use a q-tip to rub some around in your dd's nostrils. Tell her it doesn't hurt a bit, it's just slimy, like a slug climbed in her nose.
I get the most nosebleeds from dry air. Air conditioning is my enemy! I can't sit an an air conditioned car or home without being near an open window. And they're always worse in the hot summer months.