A. I wouldn't trust the urine culture test, these tests are not always reliable. on the other hand blood in the urine in addition to long term steroid treatment - the chances it is an infection are too high, so not treating with antibiotics would not make sense.
I recommend going back to your vet and insist on getting an antibiotic treatment as well as a supplement called cystopro which helps reducing bladder inflammation.
A. There are other causes possible for blood in the urine. The next step, if it has not been performed yet, would be to do radiographs of the urinary system, without and with contrast medium (cystogram), possibly and ultrasound, and if warranted by the findings, a urethroscopy/cystoscopy in order to rule out polyps, abnormal structures and tumors. Have a chat with your vet about this.
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