In Yangon there are several tourist agencies that can book a bus ticket for you to Hpa An. Your hotel will most likely also be able to help with it. We booked our bus ticket through an agency nearby the Sule Pagoda. The one-way tickets were 6000 Kyats (± 5 Euros) each. The bus is a direct line to Hpa An center, it stops by the clock tower (the central roundabout of Hpa An).
The bus, however, does not leave from Sule Pagoda, or anywhere near the center for that matter. It leaves from a bust station (kinda close to the airport), which is about 45 minutes to an hour away from Sule Pagoda by taxi. You have three options of getting there. The cheaper one is to take a regular city bus 36 from Sule station for 200 Kyats (±0.10 euro). This ride is rather slow though and could take up to 2-3 hours.
Another option is to take a minivan taxi service, which is the option we chose. The cost is 1000 Kyats per person and an additional 500 Kyats for a suit case or backpack. The ride takes approximately 45 minutes to an hour depending on traffic and how many people get picked up and dropped off on the way. It is not the most comfortable way to travel as the seats are quite small and they really try to squeeze in as many people as they can into the van. We were the only tourists on the minivan when we took it. So it is quite an interesting experience, as the locals are very interested in you and curious about where you are going to.
The last and most expensive option is taking a taxi. This will take also 45 minutes to an hour. It is the more comfortable means of transport of course, as you will not be squeezed. Nevertheless, it is rather pricy, it costs approximately 8000 to 10000 Kyats.
Once you arrive at the bust station, the next challenge will be to find your bus to Hpa An. The bus station is quite big and rather messy. There are multiple terminals, and no signs or anything that could indicate where you should go. We had to walk for about 10-15 minutes to find our bus. We asked many people on the way to make sure we were on the right track. Once in the bus, you can enjoy a long 6 hours ride to Hpa An with buddhist prayer played loud through the bus stereo. It is something typical for buses in Myanmar to play the buddhist prayers in the beginning and later-on either some Burmese karaoke music or Burmese comedy shows. You could try to ask the driver to put the volume a bit lower so you can hear yourself think.