I didn't want to buy oilcloth online, and couldnt find any local stores that sold it. However, I found a local craft store that had what they called "oilcloth" but which was really vinyl with a cotton backing - something you would traditionally use to make a picnic tablecloth.
I just sewed 2 pieces, wrong sides together, first - so that the inside and outside of the bag would show the pattern/right side of the vinyl fabric, hiding the cotton underside.
I also added velcro to hold it closed. One set to hold it shut at the top, and another set to keep it folded down.