I haven't stayed on the bottom very long, but I assume you would be limited by your transmitter battery capacity in most cases, because using a main drive battery and BEC on your sub with no functions of the sub being used, only the receiver would draw a small amount of battery current on the sub. The standard old AM or FM radio set supplies receiver and transmitter batteries of about 700 mah capacity, and I usually get about 2 hours use from a full charge.
In most setups turning your transmitter off to save the battery would activate a failsafe and surface your sub. Others may have more experience or radios similar to yours, with different capacities and durations of operation.
RCABS- It's easy to control your own bladder!