The short answer
The short answer is no, you can not. Shipping by buses and trains used to be very common for tourists prior to COVID-19. However, after COVID-19, the laws changed for bus companies, and the train line as an operation significantly changed as well. There will be plenty of out of date articles on the internet suggesting you can easily ship motorbikes by buses and train.
Tigit has a full article here: https://www.tigitmotorbikes.com/transporting-motorbike-by-train/
The long answer
It is possible to ship motorbikes by train from one location to another. However, the motorbike does not go with you on the same train. The motorbike will show up anytime from 4 days to around 10 days after the shipping date. There is no way to know the duration of travel and no guarantee that they will keep the shipping times they may give.
From our perspective, when a client starts to inquire about shipping a motorbike, we consider the contract is coming to a close. We will advise you to return the motorbike to the nearest Tigit office and book another motorbike from a different office. This is due to the quantity of time it may take for the motorbike to arrive at your final destination.
Trains that the motorbike will go with you
There are trains such as the HCM to Mui Ne train and the Hanoi to Lao Cai train where the motorbike will go with you on the same train. However, using these services requires booking the motorbike physically at the train station in advance. Overall, the system is out of date and not worth using. So yes, it is possible, but no, it isn’t of any interest!
Motorbikes on buses
Putting motorbikes on buses is illegal but very common. Because of this, the companies operating these services pop up and collapse regularly, meaning we can not recommend any particular service. It would be best if you inquired in the town directly that you wish to ship from.
A very common section of the country where people skip using a bus is Phong Nha to Hanoi. You can arrange this through your hotel.
A quick disclaimer on buses: They can do a lot of damage to motorbikes. They will not be responsible for the motorbike damage. Use these services knowing the risks involved!