"The dead bodies...are beyond recognition," Hamza Anjum, a senior official of Lasbela district in Balochistan province, said at the accident site.
Anjum said three survivors had been rescued and the bus was reportedly carrying 48 passengers when it hit a pillar on the bridge and careened off course earlier on Sunday.
It had been travelling overnight between Balochistan's provincial capital of Quetta and the southern port city of Karachi.
"It is feared that the driver may have fallen asleep," Anjum said, also mentioning the possibility the driver had been speeding during the long-distance trip.
"We will investigate the causes of the accident," he said, adding that DNA tests would be used to determine the identity of the remains which had been "badly mutilated".