The BCG is not supposed to cause an infection and rarely does in people who have normal immune systems. It does, however, cause an immune response which is the basis for using it as an immunization against tuberculosis. It's use as an immune system stimulant helps in fighting bladder cancer locally.
If the BCG were actually the cause of a UTI, it would have to be treated with antituberculous drugs. It is expected that when you empty your bladder after your treatment that you will get rid of all the BCG. If that wasn't the case, repeat instillations wouldn't be necessary... but the risks would probably be too high to use it as a treatment.
A variety of things increase our risk of developing a UTI - instrumentation of the urinary tract, even catheterization; inflammation of the bladder, an expected side effect of BCG treatment; and incomplete emptying of the bladder. Once a UTI is established, the bacteria in the urinary tract multiply more quickly that they can be urinated out so antibiotics are used. I am assuming that you doctor felt this was a routine, complicating UTI since his choice of treatment was Cipro, an antibiotic used to treat many common UTIs.