Oops. I think I've got plastic mesh confused with plastic canvas sheets. You can get the canvas sheets cheap at a craft store, and the best thing is, they come in a variety of colors, even clear (which isn't too clear, but it's a nice thought). It is very sturdy, so it wouldn't fold over, but it's light enough that suction cups would hold it up with ease. You can cut the sheets down to whatever size you prefer, or if it's for bigger fish, you can connect two pieces together ( I couldn't imagine you needing to do that though).
Instead of using twist ties, you could use fishing line and bind the corners together that way. The thing about twist ties, is that most of them have wire inside of them, and the ends are usually exposed. I'm not sure how dangerous it would be. I was always told to never put metal in tanks because it will eventually kill the fish.