Knowing what's best for the environment can be a confusing. Using the least amount of bags is best tho.
This British study, talked about here, says that plastic shopping bags might have a lower footprint on the environment than cloth. To put it another way, one would have to reuse a heavy cloth bag over 100 times for it to have less of a footprint than the cheapest plastic bags. That has to do with what it takes to grow the cotton, make the bag and so forth.
Still, I am skeptical due to the effect of discarded plastic waste in the environment, however many plastics are biodegradable. The best strategy is to reuse the bag many times, or not use a bag.
Personally, I use my bicycle panniers. I guess even folks who drive don't have to use shopping bags either. Just roll the shopping cart out to your vehicle and put your groceries into reusable containers. I bring the cart to my bicycle and load my panniers. Actually I just use the store's shopping basket as I seldom buy many groceries in one trip.
This radio interview overlooked a big elephant in the room. The automobile. What effect does driving to the store have on the environment? In my case, I live in a dense urban neighborhood so I can walk, or bike to the store each day.
Here in Bellingham, plastic shopping bags have been banned by city ordinance. Stores have to charge extra for a bag which is usually paper. I never buy the bag. Paper bags may be worse for the environment than plastic as they are heavier (more material) and they tend to degrade so they can be less reusable.
This British study also compared the impact of paper bags. It says that their manufacture places a bigger footprint on the environment than the cheapest plastic. Paper bags lie somewhere between plastic and cloth as to the impact of their manufacture on the environment.
Plastic trash bags are an issue also. I seldom use them at home
For garbage, I am fortunate living near the Bellingham Food Co-Op where there is a green waste. Food scraps that tend to turn smelly in garbage can be carefully placed in the green bin to become compost. Other "dry" wastes, like plastics, can be kept clean for recycling.
As I've written about before, biodegradable plastic shouldn't go with other plastics as that degrades the mix. I try and put that in the compost bin, or it that is not available in regular trash.
Basically, I really don't use garbage bags at home. Living close to waste bins, I separate and take things there. Some things, especially stuff made from mixed materials, I do put directly in the dumpster. No need for a garbage bag, I just take it directly there. Food waste is the worse stuff for going to the dumpster if there is no bag, but use of the green waste bin seems to solve that messy problem.
I'll admit, where I work, we sure go through a lot of plastic garbage bags. At work, I try to reuse the huge amount of trash bags they use for dirty towels. I give the bags a second life lining trash bins in my work area. (I'm a custodian at a YMCA). They tried reusable cloth bags for the dirty towels, but they don't last. They tear too easy.