Well, I know that knitting with bias-cut fabric strips has been done by many a craftster, so this isn't the most original alternative material...but do I get extra consideration for the fact that the handles are made of "not approved for use in icemakers (ummm...okay?)" clear plastic tubing from Home Depot? Pretty please?
The fabric is really cheap-looking polyester satin, but the color was soooo pretty that I had to buy it anyway. The bias strips were tied together end-to-end, and the fraying and irregularity seemed like they added to the fun texture. Cutting the strips on the bias cut down on the amount of crazy-long fraying threads, and made the fabric a little stretchy.
This was a very fast, fun knit. It was just a rectangle, then I used another fabric strip and a giant yarn needle to sew up the sides. Then, I realized that I didn't have any purse handles (or any patience), so I found the plastic tubing I had bought a while back with the intention of trying to make my own addi-turbo-style circular needles http://www.craftster.org/forum/index.php?topic=25372.120, and I used more fabric strips to gather the tops of the knitted rectangle around the tubing.
The two lengths of tubing were formed into circles with an overlap of about 4 inches, which I wrapped in (forgive me)...duct tape. To hide this ghastly makeshiftiness, I tightly wrapped more satin strips around the duct-tape covered areas of the handles and tied it in messy knots.
Of course, I realized that this purse would never hold anything, and that it would stretch out like crazy and quickly fall apart... so I used a rectangle of the satin to make a crude lining and stitched it to the handles and fabric wrapped around the handles.
It is actually very sturdy now, and fun to carry. It did grab a doorknob once, and nearly pulled me down onto the sidewalk, but the purse was fine!