'Real local floating markets' offered by tuk-tuks are often Damnoen Saduak — a tourist-trap circus 100 km from Bangkok.
If you want a floating market, take a half-day tour from a reputable agency (Klook, Get Your Guide). Amphawa floating market (Sat–Sun) is more authentic.
Don't pay tuk-tuk drivers for 'floating market private tours' — overpriced and disappointing.