The Taliban said they carried out the attack in the south-east of the city.
They have stepped up their campaign ahead of the departure of Nato-led combat troops at the end of 2014.
The latest attack is the third by the insurgents in Kabul in just over a week. On 17 January, 21 people died in a gun and bomb attack on a restaurant.
In Sunday’s attack, two soldiers on the bus and two civilians on the road died when the suicide bomber detonated his vest, a spokesman for the ministry of defence said.
The BBC’s David Loyn in Kabul says government buses carrying security forces and workers to ministries in the capital are a common sight – and an easy target.
Earlier this month, a spokesman told the BBC the militants are “confident of victory” over Nato-led forces and already control large areas of the country.
Source: BBC News
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