Yes, plastic bags can be recycled, and yes, I could be better at remember my millions of reusable bags at the grocery store, but when I get too many plastic bags; i.e. the cabinet under the sink is overflowing with them, this is what I do:
I crochet them into reusable bags. Currently I'm working on a "beach" bag. I'm not the best crocheter ever, but the plastic yarn (plarn) seems to be fairly forgiving. The most complicated part is making the "plarn". Its not even that complicated, mostly just labor intensive.
It's ultimate recycling I think, which is my favorite way to craft.