The Defense Ministry confirmed the number of casualties in a statement updating a previous toll. Army Gen. Kadamshah Shahim said the bomber was stopped before he could enter the bus, likely limiting the number of casualties.
The Taliban claimed responsibility for the attack, with a spokesman for the insurgents, Zabihullah Mujahid, confirming that the air force bus was the target.
The attack came as the country struggles through its first democratic transition of power, with one of the candidates in last month's presidential runoff alleging fraud. Abdullah Abdullah, a former foreign minister and one of two candidates vying to succeed President Hamid Karzai, has warned he will boycott the results of the June 14 balloting.
Abdullah, who won the first round on April 5 by a wide margin, says supporters of his opponent, former Finance Minister Ashraf Ghani Ahmadzai, stuffed ballot boxes and tried to rig the vote.
According to the official timetable, initial results are due Wednesday and final results are due on July 22, with the inauguration date for the new president scheduled for Aug. 2.
Both candidates have promised to sign a security pact with the United States that would allow nearly 10,000 American forces to remain in the country in a training capacity and to conduct counterterrorism operations after most foreign troops withdraw by the end of the year.
But a disruption in the announcement of election results could mean another delay in finalizing that agreement, which was rebuffed by Karzai.