By News Agency
They then targeted a police vehicle that had arrived at the scene. Somalia’s al-Shabab Islamist militia has said it carried out the attack.
Nearly 100 people have been killed in violence on Kenya’s coast this summer.
Hundreds of families have been displaced by the unrest, which has also damaged the local tourist industry.
The bus driver was among those killed, the Lamu county commissioner Miiri Njenga told Reuters news agency.
Eight people are said to have been admitted to hospital, most of them with gunshot wounds.
The attack comes a day after Kenya’s military said its aircraft had bombed jungle bases used by militants in the area.
A spokesman for al-Shabab, Abdulaziz Abu Musab, told Reuters the Kenyan announcement was “propaganda”.