If you want to work with recycled materials, start by finding out what's available locally and for free/cheap. Something akin to craigslist or freecycle listings, or maybe you have a reusable builders supply in the neighborhood. Approach those in terms of "what can make a container?" and go from there.
You could be as simple as two
sonotubes of the right diameter, or as complex as weaving some plastic strips together. Fortunately, the criteria of "will hold a trashbag" is broad enough to leave a lot of options.