I would wait till after Halloween to put it in the fridge. At that time, the days are shorter which will signal the vft to go into dormancy. Growth of new traps will be slow and traps will be smaller. Older traps will turn black. After nature puts the vft to sleep, I would remove the vft bulb and cut off all the remaining leaves (above the soil line). I then wrap the bulb with sphagnum moss (or a wet paper towel), and place in sealed plastic bag for fridge storage till Easter.
Others have suggested sealing the entire pot/soil/plant in plactic bag rather than removing the bulb. You decide!
As for your mold/fungus, remove the bag for a few days, but mist the vft twice daily (for humidity). If the mold/fungus dissappears, continue with misting method, instead of bag.