The speeding bus was trying to overtake another vehicle when it rammed through the bridge railing at around 7am, according to the police.
The accident occurred when the underage driver lost control of the bus, said a local police official quoted in the reports.
At least 20 people have been killed and 24 others injured after a passenger bus fell into a river in northern Indian state of Rajasthan on Saturday, police said.
The bus had picked up passengers from the Sawai Madhopur railroad station.
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Prime Minister Narendra Modi expressed grief over the incident and said his thoughts were with the families of the deceased.
The 15 injured have been moved to hospitals, reports said.
Giving details of the Sawai Madhopur's bus accident, Subhash Mishra, Circle Officer said that a total of 26 bodies have been recovered so far and the rescue operation is underway to find any survivors.
Both Zakir, who police said was in his 30s, and the bus conductor Shahrukh died in the accident.