Pakistan has been hit by a wave of bombings in recent weeks in response to a military offensive against Taliban militants in the northwest of the country, but Thursday's was the closest to the capital since the launch of the offensive.
Rawalpindi, near Islamabad, is home to the headquarters of the Pakistani army and other state agencies.
The city's police chief had originally told reporters that up to six people had been killed in the blast, but he later revised that figure down.
"I was at the spot and was told the toll was five to six, but later we checked with hospitals and they confirmed one dead and 29 wounded," Nasir Durrani told reporters.
Senior police officer Rao Iqbal said the bus was carrying workers from a main nuclear facility, the Khan Research Laboratories.
Policemen at the scene shifted the mangled remains of a motorcycle from beside the bus, which had its windows blown out. Another policeman carried a plastic bag, apparently containing bits of human flesh.
In a separate incident, a roadside bomb exploded as a police patrol passed by on the outskirts of the northwestern city of Peshawar, killing two policemen and wounding four, including two civilians, senior police official Safwat Ghayur said.
The army went on the offensive in the Swat region two months ago after the Taliban seized a district 100 km (60 miles) from Islamabad, raising alarm at home and among allies who need Pakistani help to fight al Qaeda and tackle Afghanistan's insurgency.
Redeploying Border Forces
The military says it is nearing the end of the offensive in Swat, but intermittent clashes have erupted as soldiers encounter pockets of fighters.
The military said on Thursday afternoon that 23 militants had been killed and 5 captured in the previous 24 hours.
But no Taliban leaders have been among the approximately 1,600 militants the army has reported killed in Swat. Independent casualty estimates are not available.
Military spokesman Major-General Athar Abbas said media reports on Thursday that Swat Taliban leader Fazlullah had been killed were not confirmed.
The failure to kill or capture leaders of the Taliban in Swat has led to fears that the militants could make a comeback if and when the army withdraws from the valley.
As the army nears the end of its push in Swat, it has begun attacking Taliban chief Baitullah Mehsud in his South Waziristan stronghold in mountains on the Afghan border.
The army says Mehsud, who carries a U.S. reward of $5 million and a Pakistani reward of 50 million rupees ($615,000), is behind 90 percent of militant attacks in Pakistan.
Abbas said the army was redeploying some border forces to an area opposite Afghanistan's Helmand province to block any Taliban trying to flee from a U.S. offensive launched there on Thursday.
Most of Pakistan's political parties and members of the public support the recent offensive, but the government risks seeing that backing evaporate if the nearly 2 million people displaced by the fighting are seen to be suffering unduly.
The looming arrival of monsoon rains threatens to bring more misery to the displaced, potentially increasing the spread of disease, disrupting delivery of supplies and forcing some camps to be moved, United Nations officials said on Thursday.
