The 48-year-old and her 18-year-old daughter and 11-year old-son were hit at the junction of Charing
Cross Road and Shaftesbury Avenue on Sunday.
They were taken to taken to St Mary's Hospital in paddington, but the woman died on monday afternoon.
Her daughter remains in a serious but stable condition. Her son is in a stable condition.
A Metropolitan Police spokesman said the woman's husband was with them, but was uninjured.
The collision happened at about 14:45 GMT.
The spokesman said the driver of the route 29 bus, which travels between Wood Green in north London and Trafalgar Square, remaind at the scene and spoke with officers.
No arrest has been made, he added.