From Chiang Rai, board a Mae Sai bound bus and tell the bus conductor that you are going to Ban Basang.
At Ban Basang, there will be 1 or 2 blue Sawngthaews (pick ups) going up to Mae Salong. The driver will normally wait for 6-7 passengers before leaving. Therefore, it would be better to reach Ban Basang early at before 830am when there are more people going up to Mae Salong. Otherwise, the fare will be higher if there are lesser passengers.
Alternatively, you can also try hitchhiking from Ban Basang to Mae Salong.
At Tha Ton, there are many yellow sawngthaews (pick ups) going up to Mae Salong. The last one leaves at 1pm.