The tusker was being brought back from a marriage function when the incident occurred on the Jaunpur-Allahabad road, police said.
The elephant crushed the mahout Mauua Pal (36) to death after he fell down and seriously injured a passerby, besides damaging the bus.
The mahout's family was then called up to bring the elephant under control, they said, adding a forest department team later arrived to treat the injured pachyderm.