I know this is a bit off topic possibly ...but I am doing a DIY household move...and I need to store some furniture in a storage facility for a few years. My understanding is the best method is to cover it with sheeting (plastic will only invite mold and mildew). I have a number of pieces to store and am wondering if anyone knows a good source of (possibly bulk) sheeting??
Big Lots used to sell thin canvas tarps back by the paint. They were too thin to work like real paint tarps so you had to double them up. They should work for your purposes though, would keep dust off and breathe. Someplace like Big Lots might have regular close out bedding sheets for cheap too. I assume you don't care about patterns and so forth. Military surplus stores used to have things like parachute cloth dirt cheap but it has become popular so is kind of pricey now.
I am not sure plastic tarps would be the end of the world for your purposes. Just don't seal furniture into "packets" that cannot breath. Cover for dust protection only? You can get plastic tarps in different weights. The really thin ones break and tear easily so skip them.
Thrift and second hand stores might have blankets. I doubt they take sheets any more.