Designing Kitchens and Bathrooms - Help with wet sheetrock in bathroom

We have a split level house and a small bathroom downstairs. When the house was built, as long as there was an exterior window, there was not a requirement for an exhaust fan. We live in VT. Winters are cold. We have had a signficant increase in vistors at our house this winter, and of course due to the cold air, they do not open the window when taking a shower.

Recently, I found that the sheetroock was soaking wet on the wall opposite the shower. The paint was streaked due to condensation. When we took the sheetrock off, the insulation paper was soaking wet. The fiberglass was not wet at all, suggesting the vapor barrier had retained the moisture. All pipes checked out okay (no leaks). The majority of the moisture is at or below the concrete line which is about 3.5 feet up on the wall. The sheetrock above the concrete (where the walls are much thicker and there is more insulation) is bone dry. Could simple condensation cause the sheetrock to have such water damage on half a wall? We ran water on the foundation for a while to see if it might be coming in a crack through the foundation and the concrete stayed bone dry. Once exposed, all of the moisture evaporated within an hour. Also, this is on only one of the exterior walls and not happening at all on the second exterior wall. Thanks for any help.

yes it is probably just condensation, you should add a bathroom vent to an out side wall probably. There are some nice ones with humidity sensors on them out now.
O'tools comentary on Murphy's law (Murphy was an optimist)