Bathroom air vent drip

I think Chris is right, warm moist air from outside is coming into the vent and condensing on the cooler inside surfaces.

Fixing this could be as easy as fixing or replacing the outside vent damper so it closes properly. You could also go for a vent damper that installs within the vent itself. And finally, you can insulate the pipe so that the vent pipe stays close to the temperature of the air flowing through it rather than the inside or outside of the home (depending on where the pipe runs).

The vent should be going directly outside, not venting inside the attic near a screen. Also, the pipe should be covered in insulation to prevent the warm humid air from cooling down so much that the water vapour condenses and runs down the pipe into your bathroom. This might be damaging your ceiling drywall, which is a pain to repair.

1. Extend the pipe through the exterior wall. Use an exterior vent with a damper, so wind does not blow cold air into your house in winter. There a a couple of different types of dampers, and the vents come in many colours and sizes to suit the exhaust pipe (can be various shapes and sizes), a 4" round vent is most common in North America for bathroom venting. This can wait until February (it's already been years, I'm guessing - so another month shouldn't make any significant difference).

2. Insulate the pipe. You can get pipe insulation that slides over the pipe. If possible, you should do this now, to stop any further water damage.

3. If your insulation is soaking wet, replace it.

4. Repair your drywall if there has been water damage. Be sure to use a stain-blocking primer before repainting the ceiling.