I believe studies have found that the environmental impact of a re-usable cloth bag is about equivalent to 150 single-use plastic carrier bags. But plastic carrier bags tend to get re-used at least once (if only as garbage bags), so you'd have to re-use a cloth bag at least 300 times before it benefited the environment. Trouble is, studies also find that cloth shopping bags get used about 50 times before being lost, broken, or forgotten.
In any case, the environmental cost of a year's worth of shopping bags is only about the same as a single cloth bag, which (I'm guessing) is about the same as a single t-shirt or pair of socks. Which suggests to me that shopping bags are negligable source of enironmental damage and not worth worrying about. Just buy one less pair of socks a year and you're even.
That said, I generally take a rucksack when shopping because its much easier to carry. Most food here is already packaged up so much that I don't find 'germs and dirt' to be an issue.
Also, charging for bags is fine if you could be sure that the money they get for them means lower prices for the food they sell rather than bigger profits for the companies. Wouldn't market forces ensure it works out like that? I'm not sure myself.