Two armed men threatened the driver and demanded he hand over money, after they got on the bus in Port Glasgow.
Police said the pair escaped with a two- figure sum of money.
The terrifying incident happened in the town's Glasgow Road, at around 10pm on Monday.
The driver was uninjured but was left badly shaken.
Both suspects were wearing dark clothing.
It is understood police are following a positive line of inquiry.
Detectives are urging passers-by who may have witnessed the incident, or who may have seen anyone acting suspiciously in the area at that time, to come forward. Call police on 101 with information.