I'm a recycler. This website does a good job explaining why I try not to use either paper or plastic bags.
Mostly, they come to us at the expense of fossil fuel in one way or another. The plastic is not recycleable, and the bags, if sent to the landfill, can't break down because of the way garbage is put in the landfills.
What to do?
If you're cheap like me, here's how to make an easy bag from a t-shirt. If you prefer good looks, try buying a string bag. If you're really rolling in dough, buy a canvas bag like this:
As time has gone by (probably the past 20 years), I've found lots of different bags on garage sales. I paid $12 for one canvas bag at an awning company from leftover canvas. I'm sure that's the most expensive one I have. I won a string bag in an herb class drawing. I have one or two grocery-store reusable bags. I don't recall how I got them.
Two challenges I face with using my own bags, 1. clerks who don't understand. 2. remembering to take the bags along shopping.
But really, remembering is number one. I leave my bags in my truck sometimes. *Eyeroll!*
But you have to be Right On the clerks or they will automatically put your groceries in plastic. It's an automatic motion. As a former clerk, I've done it myself. If they do that, I apologize, and ask them to put them in my bags. They may not like it. That's okay.
I have had clerks that I didn't alert to my grocery bags (and sometimes even when I DID tell them), bag some of my stuff into a plastic bag. And when I asked that they bag into my fabric bags, some will take the whole plastic bag and put it and my stuff into my fabric bag. I find this VERY ANNOYING and pretty rude. But consider this: I've tried asking them to put my items into a fabric bag without the plastic bag, and they throw the plastic bag away 99% of the time. And they're huffy. So you may want to consider just taking responsibility for that particular bag and just make sure the rest of your stuff goes into the bags you brought.
I put my bags at the beginning of the food on the conveyor belt, and I try to say, "Please use my bags for my groceries." If you aren't clear and you don't let them know what's going on, you'll find that they look for a price to charge you for your bags. Often clerks are on autopilot to a degree; it's' a monotonous job, let's face it. Help them out! The ones who are not, please remember their names and get in their lines again next time. Let's be groupies to attentive clerks! Thank them. Tell their supervisor how great they are. One tip is to get in lines where the clerk is older; that's not a hard and fast rule, nor is it always possible, but that's the way to bet!
Help save the world, and reduce your use of plastic bags.
One more thing: You can tell them you don't need a bag at all. All you really need is your item/s and your receipt, right? Carrying 3-5 items naked in your arms or hands is okay. Really. It is!