As a grocery bagger (don't you love first jobs?), I consider myself somewhat of an expert on the topic. Plastic bags are bad for just about everything except ease of bagging stuff. Luckily, at my workplace, we have a recycling area, which I am semi-proud to say, I usually have to empty at least twice per day. As mentioned, usually they don't get recycled as more bags, but more commonly artificial decking material. My workplace is also considering charging for plastic bags, we already offer small refunds for the use reusable bags.
As a final note, cloth bags totally suck from the point of view of a bagger. They are difficult to get stuff in the quickly. Not to say that I don't support them, I just hate them when I'm at work.
-Ethan