Perhaps the best choice to enjoy a traditional Thai floating market without the touristy push is Bang Khu Wiang. Monks arrive by boat in early morning on their daily 'tak baat' (alms round), and a variety of farm - fresh produce is offered.  

Opening Hours: 04:00 - 07:00 (every day)
 
How to get there: One option is to rent a boat from Chang Pier (in Bangkok), and ask to be taken to Noi-Khlong Om-Bang Khu Wiang Floating Market. A cheaper option is to catch a boat from Wat Chalo Pier for a 45-minute ride to Bang Kruai (5 baht), which runs every 15 minutes from 05:00 - 20:00. From there it is a 10-minute boat ride to the market. If boats don't suit you, no worries as taxis and tuk-tuks are available for hire at the market.