One of those who died was carrying a bag which contained the bomb, Police Commissioner Matthew Iteere said.
Earlier, Uganda's police chief had warned of attacks by Somali militants.
The Islamist group al-Shabab in July said it had carried out twin bomb blasts in the Ugandan capital, Kampala, in retaliation for Uganda's support for Somalia's government.
Most of the wounded were Ugandans travelling home for Christmas, Red Cross official Nelly Muluka told the Associated Press.
End Quote Jack Wachira
"When the particles hit my leg, I thought I stepped on electrical wires. Then I heard the explosion."
Mr Iteere said it was not yet clear if it was a suicide attack.
The bus driver told the BBC that a woman knocked the bag containing the bomb, which then went off. He said she was badly injured.
AS he visited some of the wounded in hospital, Kenyan Vice-President Kalonzo Musyoka said he could not speculate on who may have been behind the blast but said police were investigating.
The BBC's Will Ross in Nairobi the fact that the targeted bus had been due to travel to Uganda seems to many people to be more than just a coincidence.
Al-Shabab has in the past threatened to attack Kenya because of its support for Somalia's weak, UN-backed government. bbc