Neo-synephrin nose spray. It causes the capillaries to constrict for a short amount of time. That should stop the flow and allow the scab to start to form. It is what is used in the ER, and can be gotten OTC. You may find it now behind the pharmacy counter, however, and may need to ask.
Leaning forward, with the bridge of the nose pinched also works. As dose small ice packs along the bridge of the nose.
You can use vaseline sparingly applied with a q-tip to the passages, but obviously not to deep. That will help keep them moist and lock in what moisture they do have. Get a moist humidifier for her bedside to raise the humidity in her room. If she is on anti-histamines for allergies, then you may want to cut back as they may be drying her out TO much. There is also nasal saline wash that is very helpful for keeping things moist and is not addicting and has nothing really but saline. Once she gets used to it, she will be surprised how well she will feel when using it (called ocean nasal spray etc.) Drinking more fluids can help also.
The problem is usually caused by dry sinus passages from a variety of sources. The skin up in there, cracks from dryness and bleeds. Or is kept irritated by repeated cracking and doesn't heal well, so continues to crack and bleed. The problem isn't to control the bleeding but to re-moisten the sinuses so that they can heal and as a preventative to stop the cycle. Just stopping the bleeding doesn't stop the cycle. IF none of that helps, I would ask the doctor for some Rhinocort low dose nasal steroid spray to help speed the healing process and take care of any inflammation up in there.
I used to have exactly what you describe, and have even been to the ER because we coudln't get the bleeding to stop. This was when I was younger, now they are not so bad. If I have them now like that, then I know that I am not doing the nasal saline etc. and start again. When I was in High School, I would spontaneous have a nose bleed while in class and have to rush to the bathroom! My nose bled all the time. So I know how she feels.
I am also a nurse (15 years now) so know that the advice I offer is safe. And have been there, done that.
Good luck,
L.