機車托運 jīchē tuōyùn / scooter freight
I never finished researching this topic, but I know it is possible to arrange transport within Taiwan.
If you are leaving Taiwan and want to take a scooter with you, it is best to forget about it. Most countries have import restrictions. If allowed it will not be cost efficient. It's best to plan on selling your scooter and buying a new one at your next destination.