You could certainly try spraying the bag with a water repellent compound. Look at an outdoor store for available products. But don't expect miracles. Water repellent sprays generally work by increasing the surface tension of a fabric so the water beads up. It may slow the entry of water, but eventually the water will win.
You can also get wax to rub into the fabric to restore it's original weather resistance. Probably a better route for cotton duck material.
Nonetheless, cotton duck is generally not 100% waterproof. You have to expect it to eventually soak up water and seem a little. I really don't think a little water in the fabric is going to make any noticeable difference in your riding performance anyway. If it's raining, you should be slowing down anyway!
For protecting the contents of the bag, I like to use a plastic trash compactor bag to line the inside of my Camper Long Flap. Trash compactor bags are extra strong so the stand up to nore use than a regular trash bag.