The bomb was attached to a bicycle parked on the side of the road in Hub Chowki area, SSP Amir Farooqui told reporters.
The bus was carrying employees of the Space and Upper Atmosphere Research Organisation.
One person was killed and 23 others were injured, state-run Radio Pakistan reported.
All the victims were employees of the space agency returning home from work.
"The bus was damaged in the attack, which makes us believe it was the primary target of this improvised explosive device attack," Farooqui said.
The injured were taken to two nearby hospitals and officials said four of them were in a serious condition.
Footage on television showed that the blast caused extensive damage to the bus and blew out its windows.
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Police officials said the IED was apparently triggered by remote control.
Security forces cordoned off the area and launched a search operation. No group claimed responsibility for the attack.