Even better solution. Charge $100 to go into the grocery store and that will greatly reduce people driving to stores, shopping and using single-use bags.
Where I am, we've been under the effect of a pretty steep tax on plastic grocery bags that get noticeably passed along to the consumer. The result, from my personal experience, seems to have been a widespread adoption of tote bags. These last a very long time, 5+ years in my own experience. It has not resulted in a decrease in supermarket visits, to the best of my knowledge.
Or perhaps I'm misunderstanding your comment.
Your fine isn't tied to any externality so it is stupid.