I've fermented in a bucket with a lid & airlock, with a lid & a folded towel over the grommet, and with just a towel bungeed over the top; all worked for me. I'll often use just the towel though, it helps with aeration. I always cover it, that's just common sense to keep bugs, dust & hair out of the must. As the fermentation progresses though, I always put it under a lid (or bung) with an airlock. There are some who swear by using tin foil & no airlock, but I don't use that method, so I can't say how well it works. I'd say using the towel only makes for maximun aeration, while the lid & airlock provide the safest covering. Take your pick. Regards, GF.
EDIT: Yooper beat me to it again!