Ngapali Beach is 450 kilometres southwest of Mandalay
There is unfortunately no easy way to get to Ngapali Beach from Mandalay. No direct flights, bus, or trains between these two places as of 2019. There simply aren't that many people going between Mandalay and Ngapali Beach
From a trip planning perspective, it's best to visit Bagan or Yangon after Mandalay before going to Ngapali. There are direct flights from both Bagan and Yangon so it can make your trip logistics much easier
Option 1: Flying (best way)
Flight costs $200-$250 USD each way
There is only connecting flight via Yangon, and the shortest such connecting flight takes 16 hours. Leaving in early evening (6:30pm), spending the night in Yangon, and arriving in the town of Thandwe the next day in the late morning (11am).
From Thandwe airport to Ngapali Beach is a short $2-$3 USD taxi ride away.
I found that Skyscanner is the best flight booking site for Myanmar, you can check your options on there.
Option 2: Bus (cheapest way by far)
There is no direct bus option either
If you want to travel by bus (which costs less than $20USD much cheaper than flying), your only option is to take a bus from Mandalay to the town of Pyay, then connect to another bus from Pyay to Thandwe
The total travel time is around 36-48 hours, with 1-2 nights on the bus
Go to Mandalay's main bus station, located here, called Chan Mya Shwe Pyi Bus Station
Get on an overnight bus to the town of Pyay. This should cost you around $10 USD and you need to have enough cash kyat to pay
The bus will take 9-12 hours to travel, leaving at 6-8pm and arriving at 5-6am the following morning
At the same bus station you arrive in Pyay, you should be able to find connecting buses to the town of Thandwe, which is basically Ngapali Beach. This should cost you another $10 USD. Again, payment is cash kyat only. I don't think it's possible find schedule or prebook this bus, I couldn't find it anywhere online
The bus from Pyay to Thandwe will take around 12 hours
Once you get to Thandwe, find a taxi to take you to Ngapali Beach for $2-4 USD or ask your hotel to pick you up