Short version: Your re-usable shopping bag needs to last 100-ish trips to be more energy efficient than using disposable bags. That's about 2 years at one shopping trip a week. In our experience they last about 6 months.
So support packaging laws, but not blindly, and not to implement solutions that may make the situation worse.
BTW, we use long lasting calico bags that probably cost way more energy than the eco-bags.