Two vets have seen her and no real diagnosis. Any ideas?

I'd have the scope her airway and I'd also scope the gutteral pouch . Gutteral pouch mycosis can cause similar symptoms (and is life threatening).

Guteral pouch? That's my guess. Have they been flushed?

Could be a bad upper molar causing infection/drainage from the nasal cavity.  A good set of x-rays might help pinpoint a bad tooth.

 My mare does this spring and fall due to allergies that cause her nasal passages to become irritated and bleed.  It is not a lot of blood though just very light mixed in with thin white watery mucous.  It is both sides not one sided.  One sided x-rays and scoping is usually a good way to go. Even both sides I should add.

Yes, yes, yes! My mare did it for about a week, just a small amount and I wouldn't have even been able to tell had her nose not been white. She had a big clot on her carotid. Had that broken loose, she would've bled out. They had her in surgery within 45 minutes of scoping her guttural pouch. 

I had a horse that had random mild nose bleeds in one nostril only. It was caused by an ethmoid tumor in his sinus cavity. The vet ran a probe up his nostril and treated it with a formadehyde? mixture that made the tumor shed off.