Ngapali Beach is 300 kilometres south of Bagan on the west coast of Myanmar.
The best way to get to Ngapali Beach from Bagan is to fly. During the peak season between October and February, there are direct flights available for $110. The rest of the year you'll need to take a connecting flight through either Heho or Yangon. Connecting through Heho takes about the same amount of time as direct flights, but flying through Yangon takes a very long time
Arrival airport: Thandwe Airport, from here you can taxi 12 kilometres south to Ngapali Beach. Taxi should cost 3000-5000 kyat ($2-$3.5 USD). If you're staying at a hotel they will likely have free airport pickup services, so definitely check with them. There's apparently a bus to runs to Ngapali Beach from the airport, but I don't know the details.
Direct flight months: October - February. The remaining months of the year only has connecting flights
October - April: $110-$130 USD
May - September: $200-$250 USD
Direct (available October to February): 2 hours, morning flight
Connecting through Heho (available October to April): also 2 hours, morning flight
Connecting through Yangon (available all year round): 16-19 hours, evening flight and staying the night in Yangon
Best website to book flight in Myanmar: Skyscanner
The only alternative to flying is to take multiple buses that can take 24 hours to travel, so I don't really recommend it for most people. You should only do this if you really really want to experience the local way of travel and you have lots of time (note that this is not based on my own experience as I flew, but it's what I've gathered while researching my trip):
First you need to take a bus from Bagan to Pyay, a small town in the middle of nowhere. This takes about 8 hours. From Pyay, you need to take another bus to Thandwe, which takes 12 hours. From Thandwe, you can then taxi to Ngapali Beach
Buses are much cheaper than flying for sure. I don't know the specifics as I flew but it'll probably cost you less than $20 for the entire trip based on my experience taking buses elsewhere in Myanmar
The bus station in Bagan is located here, right next to the airport. I have no clue where the bus station is in Pyay, but since you'll be arriving by bus from Bagan, you'll just need to catch your connecting bus to Thandwe at the same spot. And once you get to Thandwe, there will be plenty of taxis and tuk tuks waiting to take you to Ngapali Beach
You don't need to prebook bus tickets in Myanmar, so if you're feeling adventurous you can just hop on the bus to Pyay from Bagan and play by ear from there on. There definitely are buses going from Pyay to Thandwe, so even in the worst case scenario you still won't be stuck in Pyay.