We used to keep them in a "killie car" type of box. Solid wood top and sides and fiberglass screening on the bottom. Just put the worms in with a load of sea weed.
Buddy of mine uses a 2 1/2 gallon bucket with a lid. He bought it at Home Depot.
He drilled a bunch of small holes to allow water in but they're small enough to keep the worms in.
Finally, he keeps a brick in it to sink it.
Works great.