She was crossing the road at 7.10am on Tuesday when she collided with a cyclist travelling down the hill.
The pedestrian was taken to Frenchay Hospital where she has undergone emergency surgery. Her injuries are described as life-threatening.
An Avon & Somerset police spokesman said: “Inquiries are being conducted to establish the circumstances of the collision. Anyone who saw what happened, or has information which could help us, should contact the Collision Investigation Unit on 101.”
Police would like to speak to the driver of a white van who stopped at the scene shortly after the collision but who left before they arrived.
Meanwhile a man in his 60s has to be freed from his car by firefighters on Monday after an accident in Siston in which the vehicle rolled over and came to rest on its wheels again.
When fire crews arrived on the scene in Siston Lane, they found the man trapped in a Citroen Picasso and complaining of neck and spinal pain.
Firefighters used hydraulic cutting equipment to remove the roof and driver’s door after stabilising the vehicle. Working alongside paramedics, the man was assisted on to a spinal board and taken to hospital.
His injuries were not thought to be life-threatening.