It's worth asking to use a bag you've brought. I do that all the time and businesses don't mind at all. Many are actually surprised and think it's a great idea.
For less planned purchases, I find it pretty easy to keep a bag in backpacks, jackets, etc. for ad hoc purchases (or carrying anything generally) to forgo one time use bags. The ones I use for everything are lightweight and foldable, and can easily fit in a pocket.
For less planned purchases, I find it pretty easy to keep a bag in backpacks, jackets, etc. for ad hoc purchases (or carrying anything generally) to forgo one time use bags. The ones I use for everything are lightweight and foldable, and can easily fit in a pocket.