Pam, sounds like maybe the water is finding another
path under the tub. Is the joint between the wall
and tub well caulked? How is the bath surround
constructed? You can use caulk with a mildewcide,
but the mildew is really a symptom of moisture
where there should be none, especially if it is
behind the caulk. If you have access to the
underside of the bathroom floor eg. via crawlspace,
check it for signs of dampness.
PS. Most people don’t run the fan nearly long enough;
I doubt this is the problem, but a humidistat control
would eliminate the possiblity.