Radical gunmen staged two attacks earlier this year that killed 60 people, devastated the tourism industry and rattled this young democracy.
Police fanned out throughout central Tunis after Tuesday's explosion, and ambulances rushed to the scene, evacuating wounded and dead.
Prime Minister Habib Essid and interior minister Najem Gharsalli visited the scene of the attack after it was cordoned off by police.
Interior ministry spokesman Walid Louguini said that at least 12 were killed and 16 wounded in what the government considers a "terrorist act".
President Beji Caid Essebsi was not in the bus at the time. His presidential guard is an elite security force that protects only the president.
Witness Bassem Trifi, a human rights lawyer, said the explosion hit the driver's side of the bus, describing a "catastrophic spectacle".
"I saw at least five corpses on the ground," he said. "This was not an ordinary explosion."
The attack came days after authorities visibly but inexplicably increased the security level in the capital and deployed security forces in unusually high numbers.
The French embassy in this former French territory was also put under high protection in recent days, after extremist attacks in Paris killed 130.
Earlier this month, Tunisian authorities announced the dismantling of a cell that it said had planned attacks at police stations and hotels in the seaside city of Sousse, about 150 kilometres (95 miles) south east of Tunis. Sousse was one of the targets of attacks earlier this year.
Tunisia's tourism industry has been hit hard this year following extremist attacks. Shootings at a luxury beach hotel in Sousse last June killed 38 people, mostly tourists, while in March, an attack by Islamist extremists at Tunisia's famed Bardo museum near the capital killed 22 people.
US secretary of state John Kerry, visiting Tunis earlier this month, pledged expanded economic and security support for Tunisia, whose popular uprising unleashed democracy movements across the region in 2011 known as the Arab Spring.
Mr Kerry said the US and Tunisia would soon begin negotiations on a major loan guarantee and were discussing expanded military co-operation, including intelligence sharing and the possible use of drones to collect information about potential threats.
A US military team was expected in Tunisia around late November to begin those talks.
Tunisia is the only Arab Spring country to have solidified a new democracy, but it is facing serious economic and security challenges.
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