I know a lot of grocery also offer the services of returning the plastic bags to the store for recycling. That's what I do if I have too many to reuse myself.
I'll admit that I do rely on plastic bags a lot when grocery shopping. Especially when you buy a lot of stuff. It makes it easier to carry everything and some stuff you just don't want to put into your own bag (AKA. raw meat).
Even though I do believe it's great that an effort is being made to reduce the harm done to the environment. I also think practicality matters in this issue too. If it's harder to carry things home, people will buy less. Buying less could possibly equal more trips to the grocery store and if you live a long distance, this means more vehicle fumes released into the environment. Public transport and privately own cars would have to accomodate to that.
Maybe it would be preferable if more attempts were made to just cut back. If you're only buying a few small items, you don't necessarily need a plastic or any bag at all.