The bomber was on foot and detonated his explosives around 7 a.m. as the bus carrying air force officers approached in the eastern Kabul district of Karte Naw, according to Afghan defense officials.
Two Afghan army officers and two civilians, a man and a woman, were killed, said Zahir Azimy, a spokesman for the Afghan defense ministry.
The Taliban claimed responsibility for the attack in an email sent to journalists.
The attack comes a week after Taliban commandos attacked a restaurant in Kabul frequented by Westerners and well-heeled Afghans, killing 21 people including three Americans. Earlier this month, a bomber on a bicycle detonated a bomb near an Afghan police precinct in Kabul, killing two police officers.
The uptick in violence comes amid growing uncertainty over the American military presence in Afghanistan beyond the end of 2014, when most of the U.S.-led military coalition is due to withdraw. The U.S. commander in Afghanistan, Marine Gen. Joseph F. Dunford Jr., is expected to recommend to President Barack Obama in a meeting Monday that a force of 10,000 Americans remain in Afghanistan to continue training Afghan forces and conducting counterterrorism operations.
But the debate over troop levels has been complicated by Afghan President Hamid Karzai's refusal so far to sign a bilateral security agreement spelling out the scope of a future U.S. mission.
Baktash is a Times special correspondent.