The 78-year-old is being treated in the Royal Alexandra Hospital in Paisley.
She was a passenger on a bus travelling on the A741 Renfrew Road in the town at around 2.15pm on Friday when it was forced to brake suddenly.
A Vauxhall Vectra Estate, thought to be a silver or grey, reportedly pulled out in front of the bus.
Police Scotland is appealing for witnesses.
The force said in a statement: “Inquiries are under way to trace the driver of the Vauxhall Vectra.
“The road was extremely busy at the time of the incident and officers are appealing to anyone who was in the area at the time to contact them, in particular, anyone with dash cam footage, as it may have captured details which could assist the inquiry.”
Anyone with information is asked to call police on 101.