The accident happened on Friday morning at the Mulibarhi intersection of Soydabad Union, Bangabandhu Bridge East Bank Police Station OC Aminul Islam said.
The deceased were identified as Belal Hossain, 35, and Abul Kalam Azad, 45.
Islam said the bike, on its way to Sirajganj, was hit by a Dhaka-bound Saikat Enterprise bus while crossing the highway at Mulibarhi.
Belal was killed on spot, the OC said.
Doctors at Enayetpur Khawja Yunus Ali Medical College and Hospital declared Azad dead after he was taken there in critical condition.
OC Islam said they impounded the bus but its driver and his assistant managed to escape.
He added that a case was filed at the police station.