The bus, which normally seats 54, had been so crowded with Hindu pilgrims that some were sitting on the roof, police said.
Initial reports suggested "the driver was drunk" and traveling at a high speed when he tried to take a steep turn Friday morning and crashed, some 100 kilometers (60 miles) north of West Bengal's state capital of Kolkata, according to Burdwan police Superintendent Kunal Agarwal.
"We are on the lookout for him," Agarwal said.
The pilgrims were traveling from Burdwan to a temple in Mayapur, where they planned to offer prayers to the Hindu god Krisha and swim in the Ganges River.
The state government said it would give 200,000 rupees ($3,222) to the families of those killed.
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