There are plastic shopping bags(worn item), and then there are just regular plastic bags(non-worn version).
The shopping bags(worn item) have the dmg indicator bars, like other worn clothing items. It must be worn/held on/in your hand, which has already been mentioned, similar to the way a backpack would be worn on your back. You can craft a “pair of bag gloves” and a “pair of bag socks” with the shopping bags, and possibly more but I do not believe I have personally crafted any of the items from them myself.
The plastic bags(non worn version) can be used for crafting recipes, arrows in particular is one I can think of that I’ve used (you can also use cardboard or feathers instead though, I believe, so they aren’t absolutely needed). You can also take 3 plastic bags and make a plastic chunk, if you have a plastic mold, which can be used in many recipes(see: http://cdda-trunk.chezzo.com/materials/plastic). Though you can get plastic chunks pretty easily by just salvaging clothing from dead zeds or at the fire station when you go to get firefighter gear or nomex patches anyway.
I am a hoarder in game so I usually just grab everything and take it back to my pile of items. That way when I go to craft stuff I usually just have it all close by, so i usually just keep them in the ‘spare parts’ or ‘other’ pile.