On reaching the Albion community in St Thomas, the argument escalated and the male passenger allegedly attacked the bus driver with a knife.
The driver, who is said to be a licensed firearm holder, then reportedly pulled his weapon and shot the passenger.
The injured man was rushed to hospital where he was pronounced dead.
The Gleaner was informed that the bus driver was an off-duty policeman and that he told investigators that he acted in self-defence.
The incident has been reported to the Independent Commission of Investigations.