For the right amount of money, you can ship anything.
You just have to be ready to pay the $$$. UPS standard shipping applies to anything you can fit in a box that is 165 inches (length + girth) or less, and 150 lbs or less. That's a box 3 1/2 feet tall and 2 1/2 feet wide and deep. You can fit a lot of bonsai in that box
Wire the pot securely to a board the same dimensions as the bottom of the box, insert bonsai into box, wire board to bottom of box, and fill completely with foam peanuts. Done.
Just be aware that there may be agricultural restrictions depending upon where you are shipping to/from.