A recent CT scan revealed bladder wall thickening, and my last two urine cultures showed "moderate" and "heavy" blood. What could this mean?

See a urologist. There are many possibilities, but a few potentially bad ones need to be ruled-out. Somebody your age with bladder wall thickening and blood in their urine should have this worked up by a urologist.
Possible infection. You could have a bladder infection or an inflammatory process involving your urinary tract. Bladder cancer would be unlikely in a patient of your age. Sometimes if the bladder is not completely distended, it can have the appearance of bladder wall thickening on ct. You should consider seeing a urologist if you have not already done so.
Need further tests. You simply may have a chronic infection, or it could be significantly more serious. See a urologist immediately, and get further evaluation.