Fred, so sorry to hear of your difficulties. And yes, you are learning one of the "dirty little secrets" of bladder cancer....it does tend to return. Do you know what your initial pathology diagnosis was? (you should have, or get, a copy of the pathologists report for your records.)
Your urologist wants to do another biopsy and "go deeper" to see whether the cancer has progressed into the muscle of the bladder. This is an excellent idea since he needs to know exactly what you are dealing with before he recommends the next step in treatment.
If the cancer is still superficial, he would probably prescribe another course of BCG. Many patients have the initial course of 6 instillations, followed by a series of maintenance doses every three months for a period of about 2 years. The maintenance regimen has been shown to have better results than just the initial treatment, but since BCG is in such short supply currently your urologist may not have had enough to suggest this.
You are in an excellent location to look for a second opinion, and now would be a good time to do it. Memorial Sloan Kettering in NYC is one of the top, as is Johns Hopkins in Baltimore. It might mean a bit of a drive, but would be well worth it.
Best of luck to you
Sara Anne