Renting your own Honda 125 cc motorbike can easily be done at the one & only Honda dealership in Mae Sai which is located less than a mile from the Myanmar/Thailand border crossing on the main road in Mae Sai. All that is required of you is that you leave your passport, fill out some short paper work, and pay the rental fee which is about $3 usd per 24 hour period. It seems to be a bit harder to rent the bike if you're a Thai citizen so its best to use a foreign passport when renting from them. They will provide you with a map of Mae Sai and a helmet.
An easy option for getting to Mae Sai would be a daily flight from Bangkok to Chiang Rai on Air Asia. The flight is a bit over an hour and cost us about $40 usd one way. From the Chiang Rai International airport you can hire a taxi or tuk tuk take you to the Chiang Rai bus station where you can catch a small bus to Mae Sai. Your other option would be to hire a taxi to take you into Mae Sai which is about 45 minutes north of Chiang Rai.
Getting to Mae Sai is as simple as catching a bus from Bangkok's main bus station to Chiang Rai. The drive up take about 10 hours overnight. At the Chiang Rai bus station there are little green local buses that say Mai Sai on their windows....these are the buses you want to take for the one hour trip to Mae Sai city. After arriving at the bus station in Mae Sai you can hire a moto taxi to take you into town or to the Myanmar border. The ride into town is about 40 baht. While in Mae Sai you can easily rent your own moto or hire moto drivers from various stands to take you around town.
The center of transportation in Mae Sai.All buses from Bangkok,Chiang Mai,all districts in Chiang Rai and others 're stop here.
From Mae Sai Bus terminal,there's a public car called "Song Taew" or 2 row of seats to the border. The cost 's 8 Bahts.