Are you sure where the blood is coming from. I recently had this problem with my elderly female cat. She was using her tray, and straining. The vet suggested putting white kitchen roll in the tray, which makes it easy to see if the blood is in evidence in the urine, as there will be a wet patch with the spots of blood. If no wet patch and just blood, then it's coming from the bowel. Tried this, and it was with the urine, informed vet, took her in, result was cystitis which is very painful and the cause of the straining. A course of antibiotics soon cleared the problem. Any stress can cause this in elderly cats. If the blood is coming from the bowel, then it needs urgent veterinary attention. Incidentally, while cat had the cystitis she didn't have a bowel movement. Hope this helps, but at least you have something to consider.