The incident took place in Benapole-Jhikargachha highway in Mollickpur area at 8am on Tuesday.
The two have been identified as Tauba, 8, and Tariqul Islam, 42.
A Benapole-bound bus from Jashore veered out of control and ran over the two pedestrians on the side of the road, said Navaron Highway Police Outpost Inspector Titu Kumar Nath.