Reply #1: The leak is most likely at the tub drain or just past it.

[here_is_to_hope]

The water may be collecting under the tub and then flowing to the vent opening, not really coming out of the vent but out through the vents hole in the ceiling.
This is a right away repair because of the damage sitting water can do to drywall and wood.
Lift the tub or gain access to it's underside, the leak should be obvious.
I don't know of any insurance that would cover this though!
Good luck!