They perished in the 1:30 a.m. accident after the City to City bus bound for Homabay veered off the road and rolled at Ntulele.
Traffic Police Commandant Samuel Kimaru told Capital FM News that 35 passengers died on the spot in the 1.30am crash.
Others succumbed to injuries in hospital.
Among the dead were more than 30 adults and four children.
Kimaru said it appeared like the 62-seater bus driver lost control before the vehicle rolled down a valley.
“The bus lost control at Ntulele. We are at the scene now and it is quite disturbing,” he stated adding that it was still not clear whether the driver survived the accident.
“We still do not know the whereabouts of the driver. We want to ascertain whether he is among the dead or the injured who have been rushed to hospital,” he said.
He also stated that rescue efforts were still underway and more bodies were being removed from the wreckage.
Those who were seriously injured have been admitted to Narok district Hospital.
Kimaru cautioned motorists against traveling at night adding that drivers who have to drive at night must drive carefully.