It was a bit east of the main line Nairobi that the accident occurred on Saturday.
A yellow school bus hired to drive, among other things, a church choir to the ceremony in the town of Kitui, tipped over and sank while the driver tried to navigate in the rolling water.
It is still unclear how many people died in total, but Kitui's governor Charity Ngilu stated during the day that more than 23 bodies had been recovered from the water.
She continued that more people are below the surface, but that the search will not continue until Sunday morning.
Some on board the affected bus managed to escape and were helped to safety.
12 people, including four children could be rescued.
Witnesses said the driver had stopped to cross the river and was near the other side when the bus was swept away by the current.