Around 15 survivors from the bus that was headed from the capital, Nairobi, to the western town of Kakamega were receiving treatment at a hospital in Kericho, Rift Valley regional police chief Francis Munyambu said.
The accident occurred in the early hours of the morning and seven children were among the dead, he added.
Mr Arome, said the bus was not licensed to operate at night and that its owners will faces charges.
“It is very unfortunate what has happened and action will be taken,” he said.
Kenya has struggled to reduce the rising number of road accidents as more people in the growing middle class acquire vehicles.
According to government statistics, around 3,000 Kenyans die every year in road accidents.
In the 2015 Global Status Report on Road Safety, the World Health Organisation said Kenyan roads are among the most dangerous in the world, claiming around 29.1 lives per 100,000 people.
In 2013 the government re-introduced breathalysers but had to remove them again after court orders barred police from charging drivers based on readings from the devices.
In an article for the online publication Elephant in November, commentator Patrick Gathara criticised the government’s “knee-jerk responses such as the banning of night buses, enforcement of speed limits, seat belts and speed governors on public transport vehicles.
“Reactionary legal measures are quickly announced in the aftermath of a particularly horrific crash, with little research, forethought or long-term planning, and just as quickly forgotten,” Mr Gathara wrote.