Forty-four bodies have been pulled out of the canal near Vadodara city in Gujarat state, and rescuers were searching for the 14 missing passengers, according to district official Vijay Nehra.
Four children swam ashore and have been hospitalized, Nehra said.
Earlier, Nehra said at least 45 people had died.
The bus driver was among those killed, said Superintendent of Police Amit Vishwanarain.
The state government ordered an inquiry into the accident and rushed medical teams to the scene, 95 miles south of Ahmadabad, the key Gujarat city.
The flow of water into the 20-feet -deep canal from a dam has been stopped to help rescuers locate the missing people, Nehra said.
The students from a village school traveling to a nearby town, Bodeli, to take an examination when the accident occurred, Nehra said.
The bus driver appeared to have lost control of the vehicle while trying to pass another bus, he said. The vehicle smashed through a concrete barricade into the canal.
Residents of a nearby village rushed in to help with rescue operations, he said.