Are there any foxtails she could have inhaled?

Foxtails occur west of the Mississippi River. No way thats a issue where the dog is. I'm in Alabama and they are not here. It's a west coast thing. Very, very bad for pups.

Dont want to be depressing, and of course you should get
the Tick thing checked first, and I suppose her allergies
could be at the bottom of it,  is just equivalent to human
Rhinitis causing bleeding, often the older people get - it
happened to me and to a girlfriend - but the only time I
have seen exactly the symptoms you describe including
the dry scratched skin on the outside of the nose, was
my dog's grandma at about 7 or 8 years, and that was a
nasal tumour.

Hope it isn't.  Best of luck.

http://www.vcaspecialtyvets.com/veterinary-referral-associates/departments-doctors/doctors/david-saylor/10146

This is the best soft tissue surgeon I know and he is in Gaithersburg. Bleeding from one nostril must always be a concern as it can indicate a nasal tumor.

Thanks for all the advice, and the Gaithersburg vet.

I talked to the regular vet and she seemed to think their blood tests have already covered infection where relevent, and that otherwise a swab of the nose could be done.  But she said they are unreliable and Tara is not having any regular discharge from her nose to suggest such a thing, just when it bleeds.  (I did not mean a spray-type repellent; Tara gets Revolution and Frontline every other week.)

So, she is signed up for an internist who does rhinoscopy.

If it turns out she needs surgery or a biopsy, keep Dave in mind. He's the east coast expert and a very good vet to deal with.I used him years ago so can voutch for him and he's a Penn grad, a big plus in my book.

Repellent? Forget it. Frontline and such work only after tick attaches it self. Then the infection is already passed. And on top of it it takes only a 1 (ONE) tick to pass the disease. 
You asked for advice but do not listen. I would order to the  vet to do  tick fever ( Ehrlichiosis). I have hard and fast rule : Nose bleed =>  do Ehrlichiosis test. 9 out of 10 times it is nothing. BUT!!!!  
Normal blood test which you have done does not test for Ehrlichiosis. All it may do is to show diminished platelets> But that is not obvious in early stages when the disease is stil treatable. You may be wasting time.   Ehrlichiosis is spread all over the world. Your area is most definitely not an exception. 
Why you resist that option? Ehrlichiosis is a spirochete which attacks different blood cells. Mainly platelets. That then causes nose bleed and other bleeding which does not stop readily. If your dog does not have Ehrlichiosis then all is good in that field and you spend  little money to eliminate deadly disease. If the dog  does have it then if not treated ( and sometimes not even then)  the dog  will die horrible torturous death from it. My suggestion is do it asap. 
I hope I conveyed the urgency of the situation strongly enough. 

Ol' Line, gotta go with Hans on this--tick panel to rule out ehrlichiosis, etc. Takes a drop of blood, tests for ehrlichiosis, Lyme, Rocky Mtn Spotted fever--all three can cause the problems your dog's been having, such as severe joint pain, in addition to the hemostasis concern, and all three need to be diagnosed as soon as possible for best response to treatment...and all three can kill the dog readily.  In the grand scheme of things, this ought to run you less than $80, is non-invasive save for drawing the tiny amount of blood, and will eliminate the possibility of a systemic disease that would not be picked up by the routine testing done for bacterial and viral infections. 

It is certainly possible that your vet did run the tick panel and has already ruled these out, but if not, it is needed. 

Again: there is NO product approved for use in dogs that has a 100% efficacy rate against ticks.  NONE.  Please don't permit a false sense of security because you've been faithfully using Frontline or Revolution [or anything else] cause you to overlook a very real possibility as to what is causing your old girl's nosebleed. 

Years ago, my eight year old female developed bleeding from one nostril. I had the scope done (really expensive!), and they found benign cysts all up one side of her nose. The vet didn't know what caused them, or what else to do. So, I thought about it and tried to figure it out myself. She was a very allergic dog, also. I figured that being in her nose, the allergy would be inhalent, and I did have cedar chips in part of her yard. I had someone come in and truck it all out, and I had hard wood chips put down. She never had another nosebleed and lived to be fifteen. Just my experience, if it can help at all.

They have a new test for tick borne diseases http://www.idexx.com/view/xhtml/en_us/smallanimal/inhouse/snap/4dx.jsf?SSOTOKEN=0

SNAP® 4Dx® Plus Test

Know more with every result.

 

The SNAP® 4Dx® Plus Test raises the standard of care for annual parasite screening. It provides an accurate result in just 8 minutes. But the benefits of vector-borne disease screening go far beyond the well-being of an individual pet.

With the addition of two new claims for Ehrlichia ewingii and Anaplasma platys, the SNAP 4Dx Plus Test replaces the flagship SNAP 4Dx Test as the most comprehensive in-house vector-borne disease screen—that’s in addition to heartworm, Lyme disease, Anaplasma phagocytophilum and Ehrlichia canis.

I wont go to a vet that does not do this test because that means they do not keep up with the current protocalls.

Also, did they make sure there is not hemangiosarcoma or other cancer?