"Forty-four bodies, most of them of children, have so far been fished out from the canal," DSP Vadodara (Rural) Amit Vishwkarama said.
Four children were rescued from the canal, District Collector Vijay Nehra said.
The Gujarat State Road Transport Corporation bus was on its way from Targol to Bodeli when the mishap occurred at 6:30 am after the driver apparently lost control over the vehicle.
Senior officials including the Collector and the DSP were at the spot, about 60 kms from here, to oversee the rescue operations.
Most of the passengers were children going to school. The bus was taken out of the canal.
The water released into the canal through the Sardar Sarovar Dam was stopped to aid the rescue operations, officials said.
Officials said the bodies have been sent for post-mortem.
Gujarat Chief Minister Narendra Modi announced an ex-gratia of Rs one lakh to the next of the kin of the victims.