Mohammad Hamid, a police officer, confirmed it was a bomb that tore through the bus in the city's Qassim market area.
"The explosive was on the bus," said Javed Iqbal Cheema, an interior ministry spokesman.
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said Rawalpindi being a cantonment area with a large military presence was a high profile target.
He said questions would be asked as to how such attacks could be carried out in a city like Rawalpindi.
Hyder said it had been raining when the blasts took place and most people were indoors. "Otherwise, the casualties could have been much higher," he said.
Mohammed Afzal, a police official, said the dead and injured had been transported to different hospitals.
The white-coloured 40-seater bus was completely destroyed and mutilated bodies lay on the street, a witness said.
Mohammad Tahir said: "There was a huge bang then I saw the bus in a mangled heap.
"Body parts were scattered across the road and there was blood everywhere."
The second bomb blast happened about three kilometres away in another market in the city, Cheema said.
There was no immediate claim of responsibility for either bombing.
Several retaliatory attacks have rocked Pakistan after the government of General Pervez Musharraf crushed an uprising by armed Islamic students at Islamabad's Red Mosque in July.