Cup Storage Question

I'm looking into purchasing a cup, I know some of them come with pouches, but I was wondering if I could use other cotton bags.

Specifically, I want to use the Vera Bradley coin purse (it's a little 4 inch by 5 1/4 inch cotton zipper pouch--I can't post a link since I'm a new member.) It would comfortably fit a cup, they are a lot nicer looking than some of the pouches the cup companies sell, and I feel like the zipper would make it more secure, yet the cotton is breathable. I also have some plastic lined pouches, I was wondering if I could use those? I would thoroughly clean and dry the cup before putting it in (obviously), but some sites say not to put it in plastic containers--would plastic lined pouches also be included in this?

Thanks!

That's weird that they say no plastic containers because I thought one of the cups came with a plastic looking case? I'm new to this whole thing but it doesn't appear the admin has been on since Feb. They are supposed to be made of this super silicon material that doesn't allow for bacteria so I don't see why the cotton bag is a must...if it's clean. Good question though because now it has me thinking. Not all of them come with bags. I honestly thought it was just a cute way to carry them around.