This is what I have for my bike. Carries my gym clothes and laptop quite well.

Since you probably don't need heavy-grade nylon, you could probably get away with getting a nylon duffel bag and some bungee cords, and doing some sewing to attach the two together. I bet you can get nylon bag material at a good fabric store.

So, perhaps a piece of plywood or something similar attached to the rack to serve as a platform, and a duffel bungeed to it? Treat the inside of the bag with scotchgard or some sort of rubberized coating for some water resistance, and presto. Bike bag.