I've made any number of hand bags and I generally use a pretty simple pattern. Figure out how many stitches wide you want it (call this X), how many stitches high you want it (call this Y). Crochet a rectangle that is X stiches wide and 3 Y stiches long. Crochet two triangles that start as 1/4 Y wide at the bottom and decrease to 4 stitches wide at the top, over Y rows. Starting at one end of the rectangle, crochet it around the edges of the two triangles. You should have about 3/4Y rows of the rectangle remaining - this forms the flap top for your bag. All you need know is a strap. At various times I have crocheted a strap (about 4-6 stitches wide), used straps off other things and used twisted wool as a strap.
The one thing to note about these crocheted bags is that they will stretch with use. To help minimize this, you may wish to consider lining it with fabric (this will also prevent small things like pens from slipping through the cracks). I offer no advice on this subject however, as my sewing skills are sadly lacking and it is all I can do to line my bags. Explainging it after would be just too much to bear.