Typically, a dog with a bladder infection will be squatting to urinate frequently and only a small amount of urine is voided each time. If your dog is urinating normal amounts of urine, it may not be a bladder infection. If your dog is urinating larger than normal amounts of urine, diabetes and kidney failure move to the top of the list of possible diagnoses. I am very surprised that your vet did not just go ahead and put your dog on antibiotics for a bladder infection since that is so easy to do and if the problem goes away, then there is no need for further tests.
Is your dog that psychotic at the vets that a simple blood draw would be too stressful? A geriatric dog should have periodic bloodwork done in hopes of catching problems early, but since your dog is showing disease symptoms, bloodwork is almost mandatory. The head tilt/vertigo, is not a good sign and should be looked into. It may simply be an inner ear infection, or a symptom of something more serious.
You need to examine the quality of your dog's life at this point. Is she still finding some enjoyment in living or are her days filled with misery and suffering? You know your dog and it is up to you to know when it is time and to then do the decent thing.