In my 11 years of cycling in Bangkok and now Chiang Mai, I have always carried a folded-up single page on which I have copied my passport page, visa page, latest entry stamp, and departure card (Form TM 6). I just stick it in the same Zip-loc plastic bag that I carry my phone in. Easy and good if there's an accident and you need to be identified. You don't need to carry your passport. In my riding time here, i have never been asked for or shown my passport while on the bike. Enjoy the cycling down there!