How do I convince my local grocery store to not use plastic bags anymore?

Just do your part and use those reusable shopping bags. Got plastic,,recycle it.
Takes a collective effort.

don't shop at stores that use plastic containers,bags or sell products wrapped in plastic - good luck in finding any , if you do be prepared to pay extremely higher prices

Look at what goes out the door. The bag is the least of our concerns. Short lived products and product packaging eclipses the bag by far. Is your trash can full of these bags or something else? We need quality products and less packaging.

You can always just do your part and use re-usable bags. However, you can't force a company nor its customer to adjust to your standard. You can help out with encouraging others to take you lead though. May be providing a recycling bin for the plastic bags to be returned to. Create and see re-usable bags, then donate the profits to an environment group.

Go through your local government and join the many cities/towns across this nation. That are banning them.

I know you mean well, and I agree.
However, you are trying to mentally force someone to do something they provably don't want to. That may be considered harassment, and you ought to be carefull, or in extreme cases may be awarded with an restraining order.

If you have made your point once, just leave it alone, and let it go.
There are worse things happening all over the world.
Try investing your time and energy in a hobby.

the way you work this is bring your own bags to use..I do it all the time.
the thing is your grocery store is probably a chain store and those decisions are made at corporate offices, not the back room of your local store.
Most all stores I have been in offer paper bags and plastic or you can bring your own reusable bags.

**** off hippie