Making your own grocery bags (or anything bags, really!) is a great way to make it whatever size you want, and whatever fabric you want (recycle!)! I made this bag a loooong time ago, using a thrift store find table linen (or was it a bed sheet?? I can't remember!) and the Jordy Bag pattern.
I obviously made the size of the bag much bigger than a handbag, and I attached the straps differently. I not only use this bag for groceries (which I've gotten compliments on) but I use it for EVERYTHING - a beach bag, a carry bag for Gromit's things when we have friends watch him, a book bag, library bag, etc!!
The best thing? This HUGE bag only cost me about $3 for the fabric and it's lasted for years already!