Police were called at 1.42pm on Friday, 3 December to a reported road traffic collision at Bath Road, Hounslow.
Officers and London Ambulance Service [LAS] attended. At the scene, two pedestrians had been in collision with a bus.
An 81-year-old woman was taken to hospital, where she remains in a serious condition in hospital. Her family are aware.
A man who was also injured has since been discharged from the hospital.
The driver of the bus stopped at the scene and there have been no arrests.
Anyone who witnessed this collision or has footage should call the police on 020 8543 5157 or 101 or Tweet @MetCC quoting 3597/03DEC.
To remain 100% anonymous call the independent charity Crimestoppers on 0800 555 111 or visit crimestoppers-uk.org.