If I am understanding your right I would store the worm castings in five gallon buckets. I find these buckets and even smaller ones since my system is tiny are very helpful for storing and playing aound with my vermicompost. Spring time however and everything goes. I use it all up. The buckets are ready for next winter. You will not need a cover. Probably the vermicompost will slowly dry a bit until spring. If it is in the basement you may not even have to add water. Any old containers you have around will be fine. No need to purchase new ones.

I use dry newspaper at the bottom of the bucket in case the VC is too wet and cover it with damp newspaper to prevent from drying out.