As you know, a great many plastic bags are still available and not banned (see what those are here).
A number of residents are reporting that customers are doubling up on the larger free plastic bags still allowed---to cite just one example--for loose produce, meat, etc......leaving none for the next customer at local markets. Also that smaller commercially available trash can plastic bags (not free) are selling out quicker than re-stocking occurs---and that as a result, people are making do by purchasing the larger plastic bags, also in short supply.
Unfortunately, there appears to be no easy answers here.
Residents who do not wish to buy the larger plastic bags for their trash--when the smaller now banned bags they reused for free are no longer available in stores---can still buy them in bulk from Amazon or restaurant supply stores.
Other than that, there isn't much more to say.
P.S. SOME STORES HAVE PAPER BAGS; OTHERS DO NOT. The county is currently considering a paper bag tax.