The incident took place late last evening when the UP Roadways bus lost control on the Bijnor-Chandpur Road and hit a buffalo cart in front of it and then hit the two-wheeler coming from the opposite direction.
All the three riders, Riyasat (35), his wife Rizwana (28) and their two-and-a-half-year-old daughter Ayesha, were crushed to death, they said.
The family was returning home in Bijnor from Bashta village, in Chandpur, where they had gone to attend a function.
After the accident, the bus hit a tree before coming to a stop. Two people riding in the buffalo cart, farmer Buddh Singh and his wife, also suffered minor injuries, police said.