It’s no problem to stick your bike on a bus or train in Thailand.
For the train, bikes should normally be checked in as cargo and not all services will have a cargo carriage so try to check the timetables the day before. On the other hand, very often station staff will overlook this requirement and help you put your bike in the aisle of the lowest class carriage.
There will be a charge for taking your bike – likely several times the cost of the ticket – but it’s still very good value. As an example, a ticket from Ayutthya to Bangkok costs 15 Baht and to take the bike is a further 90 Baht. That’s less than $4 U.S. total for a journey of over an hour.
If the train isn’t an option, there are plenty of air conditioned buses plying the main routes in Thailand. There are more frequent departures than the train and the seats are definitely more comfortable than the cheapest train seats, but finding a place for your bike can be a challenge. The luggage compartments tend to be small so you’ll need to turn the handlebars and you may also need to remove the wheels.
We once stowed our bikes in the back compartment of the bus, where there was a space on top of the natural gas canisters providing fuel for the bus. This meant we didn’t have to disassemble anything but our bikes did get a few scratches.
It’s not always clear if you have to pay or not to take your bike on the bus. Once, when we asked if there was an extra fee for bicycles, the ticket seller seemed to pluck a figure out of thin air. We offered half and she quickly accepted. You could attempt to get your bike on for free.
The danger of course is that you load everything on board and find the staff start asking for money afterwards, by which point it’s a big hassle to shop around for a different bus. For most countries we assume a bike fee of roughly half the cost of the ticket is fair for the extra hassle and space of carrying our bicycles.