Hi MVM,
Another source of quality garment bags is
https://www.kirbyallison.com/garment-bag.html.
You are right to worry about mold. Yes there is a good chance the rest of your clothing in the drawer or beyond has mold spores- whether they take hold may depend on your general humidity situation- so, look and smell :-)
Also if you are in a humid environment, definitely cloth garment bags, not that you shouldn't use them anyway.
The Laundress is a good source for cleaning products and has answers for specific situations. For dehumidifying
https://www.universityproducts.com/art-sorb.html- web site and product name. I found this by googling so it will give you some direction to shop around for yourself. My bookmarked museum supply site seems to have gone under