Reusable, eco or sustainable.
It could also depend what material they are made from.
Technically any bag can be reusable, even the one made of 100% plastic.
You can carry fabric bags on you. Of course you would not call them reusable as you don’t expect to chuck a fabric bag away.
If you are asked at the shop if you need a bag, you just reply no, thanks, I have MY OWN.
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