The bus was taking a church choir and other revellers to a wedding in Kitui County on Saturday when it keeled over and sank beneath fast-flowing waters as the driver tried to navigate a submerged bridge.
Twelve passengers managed to scramble to safety but most aboard the stricken bus were unable to escape before it was swallowed by the muddy tide.
Kitui governor Charity Ngilu said 31 bodies had been retrieved since Saturday by military divers, but warned the toll could rise further as the search and rescue operation continued.
"Today we have been able to retrieve seven. We still have more bodies in the bus," she told reporters late Sunday.
"It is very, very sad indeed. We have lost so many lives."
It remains unclear how many passengers were aboard the bus when it tipped into the Enziu River, about 200 kilometres (125 miles) east of the capital Nairobi.
Witnesses said the driver had stopped to negotiate the river, and was close to the other side when the bus was swept beneath the churning currents.
President Uhuru Kenyatta on Sunday sent his condolences to the families of the victims and urged Kenyans to be cautious on roads during the rainy season.
"Once again, the President wishes to remind Kenyans across the country to heed government advisory against attempting to cross swollen rivers especially during the current rainy season," read a statement from Kenyatta's office.