Farmers markets...reusable bags

Would newsprint paper be a viable option? I've seen produce wrapped up in newspaper and sealed with tape or tied up with twine. Or fold into large envelopes, bypassing the tape and string. I recently saw on Facebook in SE Asia (Thailand?) sellers were returning to banana leaves to package their produce.

One quick way would be to place all the veggie purchases in one single bag. I provide my own bags, and always ask for that to happen. It's not like the green beans are going to eat the carrots on the way home, or a fight will break out between the cucumbers and squash. I'd also vote for giving customers who provide their own bags a small reduction in price, and posting a sign at your site saying you do so. You could also consider swapping out your plastic bags with paper sacks. Finally, perhaps your sign could reflect the cost per bag which is added to the total cost if you must provide one. That way everyone will clearly see how their choices impact the final price as well as the environment.

At our local stores there are signs posted in the parking lots like this.

Post a notice:
Did you remember
your reusable bags?

Honestly, it works for me. Many times I forget and these signs are a gentle reminder.

Offer a small discount to those bringing their own reusable bags and/or a small charge if you have to provide disposable bags. We have an orchard near us that sells a logo'd reusable bag for $4.00 BUT every time you bring it in you receive a 10% discount off your entire order. It adds up.

Paper bags?

You might ask customers to donate bags that you could reuse- at least in California, people don't have tons of extras like they used to, but you might get some response. Also, I guess you might run into health code problems with reused bags, but it could be worth looking into.

You could do what supermarkets near me (Toronto) do.
Order reusable inexpensive bags with you farm name and maybe contact info on them. Sell to customers.
Also give them notice (about 4 weeks) when you will no longer provide few bags.