We've had our ban since last July, and many stores have put LARGE signs reminding people to use handbaskets or carts and not
their reusables for shopping, for this very reason.
I often carry my bag, because if I put it in the handbasket or cart it of course ends up at the bottom which makes it difficult to fish out at checkout. Of course, my bag I'm carrying is balled up in a wad and is very obviously empty.
i dunno about plastic-ban areas but here, we still ahve plastic bags for product etc - cos you don't want a bunch of grapes dancing on your other groceries willy-nilly. some stores also have them in the meat dept but if they don't then we just use the produce onces
With our ban (and many others I'm sure), plastic is banned in retail stores at checkout but the small bags for produce and meat are exempt from this.