The second attacker at another location in the city blew himself up at an army check point, injuring three security people.
In the bus attack, local TV channels reported the vehicle was carrying employees of Pakistan's Inter-Service intelligence when it came under attack near its headquarters known as "Hamza Camp," Xinhua reported.
GEO TV reported the suicide attacker rammed his explosives-laded vehicle into the bus.
Other Pakistani media reports quoted Pakistani military spokesman Waheed Arshad that the bus caught fire, killing 15 passengers on board. It was not clear how many were aboard the bus or how many escaped.
The Voice of America put the dead at 20.
More than two dozen people were reportedly injured in the twin attacks.
Rawalpindi was Pakistan's capital before nearby Islamabad took its place. Since then, Rawalpindi has become a garrison city.
No group had yet claimed responsibility for the attacks, but the BBC reported such attacks are often suspected to be the work of pro-Taliban militants to retaliate Pakistan's military operations in its restive tribal areas.
The attacks come in the midst of Pakistan's political and other problems brought on by the imposition of emergency rule by President Pervez Musharraf.