I fold them. I segregate them into piles. Coles/Woolies/Aldi/miscellaneous/ and I put them back into my car. I keep 2 calico bags in my handbag.
My folding technique is this: fold the bottom of the bag to the top, then fold into thirds so the handle is sticking out. Then I place them into a calico bag. Then they all get put into a Best and Less material bag vertically with the handles sticking up.
like this.
My husband likes to fold them into tiny little origami parcels which fucking irritates me.
I was the same until I got those nylon reusable bags that fold up to a really small size. I've got several in my backpack. The only problem is those chiller bags.. when I decide to spontaneously buy refrigerated or frozen goods I'll often buy one of those if it's hot, as my stuff won't survive the bus ride home. I've got many chiller bags at home that I'm using as storage for other things 😔
First, prevent accumulation of more bags. Is there something that would remind you to take them? Eg if you use a car to go to the shops, put them in the car. Or if you normally carry a bag or backpack, put some in there.
After that, if you have more than you can use, and they are in good condition, you could give them to a food pantry. Or, if not, reuse as rubbish bags. Unfortunately there is no soft plastics recycling anymore.