The incident occurred on Amta-Udaynarayanpur Road when the bus was going to neighbouring Hooghly district, police said.
Locals and rescuers brought the bus out of water and sent the trapped passengers to hospital, a police officer said.
While one person died on the spot, 35 others were sent to hospitals in Uluberia sub-division, the officer said, adding, five of them were stated to be in serious condition.