The mangled wreckage of the bus lay in a large crater, and the scene was spattered with blood, a photographer for the AFP news agency said.
Mian Iftikhar Hussain, a provincial government spokesman, said 14 people, mostly air force personnel, were killed in all, and another 12 people were wounded.
The girl who died was in a nearby vehicle, Nisar Khan, a Peshawar police officer, said.
The air force lorry was travelling between the city and the nearby air force base in Badaber.
A Pakistan Air Force spokesman said the vehicle was transporting rations from the base.
The explosion tore a large hole in the bridge, reducing the lorry to a wreck.
Planted under bridge
A bomb disposal officer at the scene said the device was planted under the bridge and contained between 30 and 40kg of explosives.
Rehman Malik, the interior ministry chief, said al-Qaeda-linked fighters were probably behind the attack.
Separately, Pakistani army gunship helicopters shelled suspected fighter positions in Bajaur.
The shelling struck a house in Takht village, about 10km south of Bajur’s main town of Khar, killing five suspected fighters and wounding three other people, a local intelligence official and a resident said.
Said Khan, a Takht resident, said the house was believed to be a gathering point for Taliban fighters.
Officials have said at least 100 fighters and nine paramilitary troops have been killed since last week, although independent confirmation of the toll has not been possible.
Thousands of residents have reportedly fled the area.
Meanwhile, Pakistani officials said they are investigating whether a suspected fighter reported killed in the clashes in Bajaur was a senior al-Qaeda commander.
A senior interior ministry official confirmed on Tuesday that authorities were investigating the identity of the man, identified by a senior intelligence official as Abu Saeed.
An Egyptian, he is believed to be a close aide of Ayman al-Zawahiri, al-Qaeda’s deputy leader.
A senior al-Qaeda commander in Afghanistan, Mustafa Abu al-Yazeed, who had appeared in videos issued by the group, is also known by the alias Abu Saeed al-Masri.