My first thought for construction is to lay one strip next to another, slightly overlapping, over and over until I have a sheet, then to put strips of duck tape going the other direction (criss-crossing, if you will). If I space out the duck tape strips, it'll retain flexibility, but should (in my head, anyway) be sturdy enough. That'll give me a sheet of "fabric," and from there I'll have to cut and shape as you would with regular fabric.
Does that make sense?
At any rate, as for the dress itself, a pattern might be a good idea. It would give me some idea what I have to do.
I keep thinking of oddball ideas like having little caution tape streamers hanging down from the hemline, and I have to remind myself that there has to BE a hemline first.
I might have a bit of a job in front of me.