This is my procedure for shipping plants:
Take the plant out of its pot.
Strip off the soil on the sides to make a circular plug with the plant's roots in it.
Wrap the plug in very moist (almost saturated) paper towels.
Put plug inside of one (or two) ziplock bags.
Tape ziplock bag to the back of the box.
Take plant our of pot.
Rinse off ALL extra soil and wrap plant and roots in very moist (almost saturated) paper towels
Place paper towel covered plant inside of one (or two) ziplock bags.
Tape ziplock bags to the back of the box.
Tape down ALL soil.
Cushion top growth with moist sphagnum moss and/or paper towels.
Put an appropriately sized deli cup on top of the plant, covering up top growth.
Wrap moist paper towel on the bottom of the pot and tape it down.
Put potted plant into one (or two) ziplock bag(s).
Tape bag(s) to the back of the box. Make sure to do this step especially if you're shipping potted plants with bare root/plug plants. The potted one can roll around and squish the others. It's similar to shipping a bowling ball with a bunch of eggs in the same box LOL
For all of these, add padding (crumpled up news paper, bubble wrap, packing peanuts) to make the plant(s) nice and snug
I've used this general guide for all my plants I've ever shipped (around 100 boxes, maybe 300 plants) and not a single one has arrived damaged or dead.