Yangon is the biggest city in Myanmar.
You need to get close to the Aung Mingalar Highway Bus station.
Buses number 42 and 48 go there from the Sule Pagoda, but they don't use Arabic numbers so you better ask someone about the main bus station. It will take you a while to get there.
Bus 36 leaves from the north side of the Pagoda and headed directly north up Sule Pagoda Road. It will get you to the Aung Mingalar Highway Bus Station.
Get off the bus close to the bus station, but don't go there. Just follow the main road (Thundhamma Road or Road No 3) and get to the nearest traffic lights. You will see them from the bus stop. Behind the traffic lights there's a wide roadside and good place to hitch.
You can easily catch a car to Naypyidaw or even straight to Mandalay. If you go to Mae Sot you can take a car only to the beginning of the highway and then turn right. There are also many good hitching spots.