The collision happened just before 17:00 BST on Tuesday near Bond Street Underground station. The driver of the number 73 stopped at the scene and has not been arrested.
The woman was taken by air ambulance to hospital with head injuries.
It is the second incident in two days involving a bus and a pedestrian in the same place.
On Monday, an 82-year-old man was hit at the junction of New Bond Street. He is in a critical but stable condition.
London Mayor Sadiq Khan has announced he is looking into making Oxford Street a pedestrian-only zone.
The move is part of his plans to make the area less polluted, and to create a "tree-lined avenue from Tottenham Court Road to Marble Arch".
In his manifesto, he said he wanted to start with car-free days before making the area fully pedestrianised.
A 73-year-old woman is in a critical condition in hospital after she was hit by a bus on Oxford Street.