For one season of growing they don't break down, jute breaks down slow, like rope, and the burlap provides aeration to the roots. Next season you get new ones and they are readily available free. The best ones are from coffee roasters because they were not used in nurseries. For non-green bags, get the blue bags at Ikea for 99¢.
PS. With burlap you'll need a roll of twine to shape the bag. Basically fill with the soil you need, have someone hold it up, tie cut lengths around, roll the rest down leaving a lip, and tie once more.