Anderson flats are a nursery container with a mesh bottom that are commonly used when initially potting freshly collected pre-bonsai material, known as yamadori. These containers come in several sizes, but you will want to look at the ones labeled for deep propogation. These containers will be square in size from 14.25" to 17" wide and 4" to 5" deep, with mesh bottoms containing 3/16" openings.
You will want to use a coarser aeration layer of soil (1/4 - 3/8" particle size) at the bottom of the pots so that your soil does not fall through the 3/16" openings. Randy Knight also advocates that you can use a very thin layer of coarse sawdust to help keep your soil inside the box.
As these are plastic containers, they have a tendency to bend when lifting them. This is not ideal for keeping the roots immobile, so take care when moving your containers. In some cases, you may wish to wall off parts of the container with thin wood boards to minimize the space available for your roots to grow during recovery and to provide extra stability for the container.
Stuewe and Sons
Located in Oregon, this company specializes in nursery containers. You'll want to order the AFLAT5 (15.75" x 15.75" x 5") or the AFLAT4 (17" x 17" x 4") at a cost of approximately $4 per container. Keep in mind that shipping may cost about as much as each container, and that's if you order more than one or two. Ordering around 10 containers seems to be the sweet spot for minimizing total cost per container to about $7 each including shipping.
American Bonsai Grow Containers
These appear to be rebranded Anderson flats that are 14.25" x 14.25" x 5" and cost between $10 - $15, shipping included.
Anderson Pots: Anderson Flats
Order directly from the manufacturer, but you might have to order an entire pallet. You are looking for the deep propogation containers with part numbers 2401B or 2405B.