Transport for London (TfL) has said that the incident took place aboard a route 5 bus on March 15 last year.
This service travels between Romford and Canning Town via Barking.
The passenger died in hospital from injuries sustained in the fall around nine months later, on December 30.
The incident was revealed in a report set to be presented to the TfL board next week.
Other fatal incidents mentioned in the document include a fall that took place on January 14 this year, as a Croydon tram negotiated Reeves Corner.
The passenger died in hospital earlier this month, on March 8.
A woman also died on February 8 after a car collided with a stationary bus in Lea Bridge Road, Clapton.
Around two weeks later, another car collided with a stationary bus in Bessborough Road, Harrow.
Pedestrian Chithra Vanmeeganathan was hit in the crash and later died as a result of her injuries. Two other pedestrians were also taken to hospital for less serious injuries.
Also mentioned is the fuel spillage at Thornton Heath bus garage on February 18, which caused diesel to enter the River Wandle.
In the report, TfL says: “Any pollution into London’s waterways is completely unacceptable and we will play our part in tackling river pollution both from roads we control and our vehicle fleet.
“Safety is the priority in everything we do, and it is neither inevitable nor acceptable that anyone should be killed or seriously injured when travelling in London.
“We remain committed to delivering our Vision Zero action plan to eliminate all deaths and serious injuries on London’s transport network by 2041, and our bus action plan, which set out our priorities to ensure no one is killed on, or by, a bus by 2030.”
