Regular bus services connect Mae Hong Son with Chiang Mai (Arcade bus terminal) and the entire trip will take at least 7-8 hours. A better option is the minibus, also leaving from Arcade in Chiang Mai, which only take 5.5 hours but cost 250 baht. If you're going by bus, you can choose the northern (Pai) or southern (Mae Sariang) route. The northern route is a little faster. The new bus station is about a 15 minute walk from the center of town to the southwest. The bus station is set on a seemingly deserted street that runs parallel to the main road in town.
There is also an overnight bus to Bangkok's Northern Bus Terminal (Moh Chit) which takes about 15 hours.