An extra charge to 'buy' the bottle would likely be a more effective incentive for me.
The only real solution is to have this stuff made from biodegradable materials.
It's 10% of the cost of the drink.
Just seems you're not super great at personal finance, is all.
Technically, it does reward folks when they don't take a plastic bag by not charging them. But the goal is to actually discourage people from taking one in the first place, so something that seems like a small penalty does this more effectively. You notice each time you forget to bring a bag with you, unlike the rewards. And it is universal.
Sometimes you want to reward folks, though - this works with plastic and glass recycling here in Norway. I save up most of this stuff at home and take it back to the grocery store, where I get a bit of money for most plastic and aluminum beverage bottles and some glass ones (mostly beer). If there weren't a reward for bringing it back, I'd just stick these in with plastic recycling or regular trash. This adds up so long as I don't take them in one at a time, something I can't get with a reusable plastic bag discount.