I would like to find a non-disposable alternative to plastic wrap for when the dough goes into the fridge. Can I just put in a storage container,...

Thanks, everyone. I use a dish towel for the risings, but my question is more along the lines of longer-term storage in the fridge. The author of the recipe says the dough can be stored for a couple of weeks, and I wonder if it will suffer from not being very tightly wrapped (even though I don't really intend to leave it for more than a few days). I'll try the storage container and brushing the surface of the dough with oil, which totally makes sense in terms of keeping the dough from drying out.

oops! Forgot to mention that the reason I wouldn't like a closed container for rising bread, it that would limit the dough's capacity to rise. A "lid" that rises with the dough gives it more room to express itself.

Long before disposable wraps were around, bakers put their dough to rise either in a lined basket or a large mixing bowl and covered them with a tea towel. Still works. :)

By non-disposable, do you mean reusable? Sure, put it in a storage container with a lid, and also be sure to lightly oil the surface of the dough before refrigerating it.

I have used a dry and clean wash/dish cloth without problems when working with bread dough (rising for 1-3 hours), and also pizza dough.