Local villagers fished out 14 bodies from the pond next to the road in the small town of Raghavpuram, said S.A. Huda, state director-general of police.
Police and volunteers helped rescue some of the children from the bus, which was partly submerged. There were at least 40 children in the bus when it crashed, Huda said.
The bus driver lost control of the vehicle when he swerved to avoid a head-on collision with a motorcyle, Huda said.
Raghavpuram is about 150 miles (250 kilometers) east of the state capital, Hyderabad.
India has the world's highest road death toll, with more than 110,000 people dying each year in accidents commonly caused by speeding, overcrowding and poor vehicle and road maintenance, police say.