A fundamental issue is how you rest the instrument when you have bars of rests? Also when taking a break.
Do not lay the instrument horizontally across your lap - this will lessen the tendency for water to collect in the bore or worse run back towards the bocal. Neither should you lay the bassoon down across your chair or on a shelf or floor when taking a break. Always stand the bassoon in a corner without the bocal in place (narrow end down the bell is OK). Never stand it on a flat wall - it can slide sideways and crash. Better still swab it out and lie it in the case (horizontal is OK here, as the water has been swabbed out).
Another "solution" (literally) is to take the wing joint to your kitchen sink. Mix a very weak solution (no more than 10%) of liquid dishwashing detergent and warm water. Hold the wing with finger holes uppermost and dribble the solution down the bore (easiest from the wider end) - let it make a track and run out the other end.
This acts as a "wetting" agent which for a while at least will form a slick track down which water will prefer to flow as opposed to gathering in beads all over the bore.
This is a tried and true technique from the recorder world (in fact Moeck used to provide a weak solution of "anticondense" as they called it). Flowing it through the narrow windway of recorders lessened the beading of water which in a recorder can totally block the windway and prevent the instrument from speaking.
I believe it is the total opposite of Yoshi's liquid silicon which will make water bead - that's why you mustn't get silicon in the bore. In the tone hole silicon will act as a barrier to waterflow. Hopefully all these strategies will reduce or eliminate the problem.
Your bassoon is quite possibly plastic but these days all bassoons have plastic or rubber liners down the wet side. This means the techniques are valid for wooden bassoons too.
If all fails move to a drier climate
Christchurch New Zealand
Bassoonist / Teacher / Conductor