Government plastic bag bans seem to be on the wane after Los Angeles famously banned plastic bags at supermarket checkout lines.
Instead of government involvement, this is a job for citizens. Plastic bags are very durable. In fact, that's the main complaint about them as they don't deteriorate as they adorn the countryside. But that durability is also its advantage. The can be reused many times.
At least locally, volunteerism proved to be the solution. A few months ago many vacant lots adjacent to popular stores looked hideous with plastic bags waving from the mesquite bushes. Keep Midland Beautiful held a clean-up day which brought out hundreds of volunteers to pick up and haul off litter. Vacant lots were returned to their natural state of weedy beauty.
Citizens pitched in and it paid off.
For a discussion on the subject between environmentalist Michael Bolinder and libertarian Nick Gillespie see NPR's Do Plastic Bags Bans Help The Environment? in which Gillespie makes the reasonable point that there should be a pretty high bar for government interference with commerce, choice and lifestyle.