You could find a container of the appropriate size at a thrift store. We use a big Tupperware container that we used in the past to soak our dive gear. I drilled holes in the sides for air circulation. Also drilled holes in the bottom, and the worms found their way in making it a combo compost/worm bin. When I turn the stuff, there are gobs and gobs of worms loving life in there.
Hardware cloth enclosures work well, too. If you have the space, you can build a 3-sided enclosure using pallets (find them scrapped near shipping/receiving areas). Line it with the hardware cloth to keep the compost in.
One lesson I learned with bottomless piles is that if you put them near trees or shrubs, the roots of those guys like to grow up into the pile, making it difficult to scoop out when it's ready to put in the garden.