Two trains go from Mandalay to Naba where you have to change to a bus or a pickup tricycle, US $ 17 for upperclass, uncomfortable, one arriving 11 pm, the other at 5 am. The bus in most likely full by the time you get out, the tricycle wants to be chartered, but if you are persistent you can share it with other people, 1000 Kyat ?, 45 minutes to Katha
Every second day, 5 am from and to Mandalay, 12 hours and more if you get stuck in a sandbar or delayed by fog. 36000 Kyat, seat only.
There are also Inland Waterway boats every 2-3 days, going Mandalay to Bhamo, much slower, but with cabins about US$ 60, and cruise ships for US$ 1200.
Every day from and to Bhamo at 9 am, 7 or more (if you get stuck in a sandbar) hours, by Express boat, 15000 Kyat.