We're certain that if this condition continues, you will be asking us how you can remove a bumper crop of mildew. The condition you are relating is an excellent environment for mold and mildew to prosper in. If you take our advice today the only sweating that will go on in your home will be that which is generated by home improvement tasks!
It is apparent that you have a condensation problem created when someone is bathing or taking a shower. This comes as a result of too much humidity in the air. The hotter the shower and the colder the day, the more condensation or "sweating" occurs. Your best bet here is to improve the ventilation by installing an exhaust fan at the bathroom ceiling. Proper ventilation performs two important functions: comfort control and moisture control. These devices simply provide an access between interior and exterior spaces. Their effectiveness depends on the volume of air that they move. The Home Ventilating Institute suggests that a bathroom fan provide at least eight air changes per hour. To find the fan capacity you need in cubic feet per minute (CFM), multiply the square footage of the room by 1.1, assuming a standard eight-foot ceiling.
Exhaust fans are inexpensive and easy to install. Most major hardware stores or home improvement centers will have just what you're looking for. If this is something that you feel might be a little over your head, a quick call to your local heating or electrical contractor should solve the problem.