Rosie,
My insurance is through the ACA, I have the same diagnosis as your boyfriend, and I have just gone through the 2 TURB's, and just had my 2nd instillation of BCG. My hospital said they get it when they get it, and that they'd schedule me for my treatments when it came in, but usually it's around 6 weeks from their supplier. Because your boyfriend will have his 2nd TURB in 6 weeks, and then it's likely there will be another 6-8 weeks of waiting until BCG treatments would start, I would think they would have no accurate way of being able to forecast that far ahead. I'd push back, and don't be afraid to ask for a 2nd opinion on the BCG.
...My urologist had nothing to do with the ordering of the BCG - This was done by his staff. I'd talk to those person(s).
...He doesn't even do the BCG instillations - This is done by a nurse.
Happy Thanksgiving! Hang in there!
Mike