Ok, well, maybe not the Shinkansen, but rail travel in Myanmar is possible, but I would struggle to call it comfortouble. It is, on the other hand, very affordable.
Most guidebooks will tell you that you must buy tickets in US dollars and foreign prices are 3 to 4 times higher than locals. As of April 2014 this is no longer true. Locals and foreigners pay the same price and they both pay in local currency, kyats.
Here is the Bago train station. It looks a little different than say Kyoto or Hiroshima central stations! Even Churchill station in Northern Manitoba would be a step up from this!
There is actually a safety line there, it’s very faded. It was drawn by the British when they built the station and has never been repainted since. There is a bridge to cross the tracks, but nobody uses it, they just walk across the lines. These trains move so slowly anyway, there is not really a safety issue.
Vendors sell food and drinks on the platform, as well as on the train.
There are two seating options, ordinary and upper class. Ordinary class just has wooden benches that only face one way. Upper class has padded reclining seats that can be turned around. Some of these cars are 50+ years old. They are generally pretty grubby and most of the time the seat is stuck in a reclined position. Even so, you can get up to walk around and stretch your legs and you get to see some scenery from the open windows and doors.
Train or Bus?
So, which is better? In my opinion, there is no good ground transportation in Myanmar! Both buses and trains are slow. Buses are very crowded, but trains are not. Trains are cheaper, but usually slower. In general, travel in Myanmar takes a lot of patience. Late trains and buses are very common, as are breakdowns. Track switching is manual here. The train must stop and the driver manually moves the track switch and then continues on.
I suggest if you travel Myanmar, you should try both options.
Other choices
There are 2 other options if you want to spend a bit more money. You can hire a taxi for long distance travel. You must pay the driver for both ways, since he must come back empty. This may make sense if you travel in a group.
You can also fly, but only between major hubs; Inle lake, Bagan, Mandaley, Yangon. Generally there are one or two flights per day. One way flights come in at about $100.