Dirty ones keep wet in a plastic bag until you can wash them. No longer than 1 day unless you like mold. New or clean ones I keep dry in another plastic bag until need to use them.
The longer you take to wash them, the harder it is to get them clean.That's a myth... there won't be mold after a day. I have had used dirty pads for 4-5-6 days and nothing happens to them. Don't discount all that chemistry that is used to do the actual cleaning of the carpets with those pads. Often loaded with oxidizers and other chems.... I don't think mold is really going be a problem after a day.