Till 7:00 pm, rescuers fished out 36 bodies even as four cranes pulled the bus out of the canal, which flows into the Jalangi river, a tributary of the Hooghly.
Three of the dead were children, 14 were women and 20, men. Nine persons swam to safety after the incident which took place around 7 am.
District magistrate P Ulaganathan confirmed 36 were killed in the accident.
The toll is likely to rise as the North Bengal State Transport Corporation bus, headed from Domkal to Murshidabad, had more than 52 people in it, according to those who survived.
Rescue efforts continued late in the evening with the help of floodlights.
There was confusion over the reason of the accident. While some claimed the driver was trying to overtake another bus, others alleged the driver was speaking on his mobile phone.
Soon after the incident, locals clashed with police over alleged delay in rescue operations. Angry villagers torched a police vehicle, vandalised another and even threw stones at a fire brigade. Police resorted to baton-charging and fired teargas shells to control the crowd, and called in disaster response forces.