They have boxes at the post office. Not sure of sizes.

I have shipped plants, I pack wet newspaper around the base on top of the dirt, then cut a small circular piece of garbage bag and wrap that around the base to keep dirt and newspaper in. You can pack using newspaper and plastic bags to keep plant from sliding around in box. I use a small enough box to keep plant tightly enough packed so plant does not get damaged.

I'm a regular over at GardenWebs plant trading forum. We ship plants all the time. It's quite easy. Here's the tips most traders use...
Use priority mail and ship on a Monday. You don't want the plants left in the back of a hot truck over a weekend. If you ship early in the week and use priority mail, they get there by Wednesday.
The priority mail boxes are free and come in various sizes, smallest being about $6 to send.
Morningloree is right...wrap the root ball in wet paper towels, then cover that with plastic. Leave the greenery uncovered. Stick it in the box. When the postal worker asks you if there's anything perishable inside, say yes.
That's how it's done on the trading forum and all works out fine.
Lori