The bus was about to leave a bus station in the centre of the Iraqi capital for Nassiriya in the south of the country when the bomber got on board and detonated his explosives, they said.
The bus was completely destroyed in the Thursday blast and two nearby stalls selling food and drinks were gutted as the explosion sent shrapnel flying into the air.
A security source said “there were 30 dead and 25 wounded”. All those killed were civilians.
Some bodies were charred and the bus completely burned, police said. Iraqi rescue workers could be seen dragging bodies out of the wreckage.
Blood covered the ground and pieces of shrapnel were littered across the area.
The attack came exactly a week before Iraqis go to the polls to elect their first full-term parliament since the fall of Saddam Hussein.
Security forces are bracing for a spike in violence in the run-up to the vote.
Firefighters removed charred
Two days ago, two bombers killed at least 36 people at a police academy in Baghdad in one of the worst attacks of its kind for weeks.
Earlier on Thursday, three Iraqi soldiers were killed and another two injured when armed men in two vehicles opened machinegun fire at a patrol in Dur al-Sud quarter near Iskan district west of Baghdad, an Iraqi journalist told Aljazeera.
The journalist also said the commander of Rasafa rescue police, Colonel Hussain Abd al-Wahid, escaped as assassination attempt when unidentified attackers in al-Bayaa district shot at the vehicle he and his guards were driving in.
Abd al-Wahid and three of his guards were wounded.
Aljazeera has also learned from a police source that three members of Muqtada al-Sadr’s movement have been killed by armed men in Arab Jibour in al-Dura district, south of Baghdad.