The victims were Nepali nationals on their way to the Canadian embassy where they worked as security guards.
The attacker waited for the bus as it left a compound, police said.
The blast was followed by a separate bomb attack on a market in Badakhshan province that killed at least eight people and wounded 18.
The Taliban said they carried out the Kabul bombing, the first such attack since the start of the holy month of Ramadan.
The bomb went off shortly before 06:00 local time (01:30 GMT) on a main road leading out of the capital towards the city of Jalalabad.
The guards were employed by a private security company, an official told AFP news agency. At least eight other people were injured.
The incident follows a suicide attack on a bus near Kabul last month and an attack on a court in Ghazni in June. Both attacks were claimed by the Taliban in revenge for the execution of six prisoners.
The Taliban have been waging an insurgency against the government since 2001. Nato ended its combat mission in December 2014, although about 13,000 training and counter-terrorism troops remain in Afghanistan.
Peace efforts have stalled after the Taliban refused to participate in new talks with the Afghan government until foreign forces had left the country.

Its operating profit was $559m in the three months to 30 June, down 2.5% on the same period last year.
The company found its core search engine business less profitable in a more competitive market.
Baidu announced last month that it would be investing more in its e-commerce and electronic wallets.
Research and development costs attributed to its new investments jumped 56.2% in its second quarter to $437m.
The company had a revenue of $2.67bn over its second quarter, which is a 38.5% increase compared with last year.
Baidu's financial officer said: "We continue to invest decisively in the 'Next Baidu'. We are delighted by the progress we have achieved and are confident that these investments will generate long term shareholder value."

The Exiles are bottom of the table following Saturday's 2-1 defeat against Mansfield Town, and are six points adrift of safety.
"I know we've got a lot of work to do and I know we've got to win football matches," Westley said.
"But honestly I think we're capable of winning football matches."
Ryan Bird had given Newport an early lead against Mansfield but Krystian Pearce levelled for the home side.
County's Jaanai Gordon was sent off for a second yellow card before Shaquile Coulthirst's penalty secured Steve Evans' side the win.
Newport County had been unbeaten in five games before defeat at Cambridge United and although they secured a point at home to Morecambe, lost at Mansfield.
The Exiles host the side one place and three points above them in the relegation zone, Leyton Orient, on Saturday
"It doesn't matter who we win the points against, we've got to go and win some football matches," Westley added.
"We'd been on a good unbeaten run until we lost at Cambridge and reacted well in midweek to earn another hard earned point.
"I think the lads have come together really well and it's good that we've got a clear week ahead of us because one or two of the knocks can clear up.
"We've got some good footballers here and we've been in a good run of form on the whole."
A suicide attack on a minibus in Kabul has killed at least 14 people and injured several more, Afghan authorities say.
[NEXT_CONCEPT]
China's biggest online search engine Baidu missed analysts' expectations as profits took a hit from investment redirected elsewhere.
[NEXT_CONCEPT]
Newport County manager Graham Westley is confident his side can secure the points needed to pull away from the League Two relegation zone.