The 74-year-old was on the bus in Silverdale, about 30km north of Auckland city, about 10.30am on Friday, police confirmed.
"She noticed that a wallet had been left behind by a previous passenger and had gone downstairs to give it to the driver," Acting Senior Sergeant Nick Herd revealed today.
"It is at this time that she has fallen."
An ambulance transported the woman to Auckland Hospital, but she died of her injuries.
"This was an absolute tragedy for this woman's family and our deepest sympathies are with them during this difficult time," Herd said.
WorkSafe said the passenger died on Friday after they fell down the stairs of a Ritchies bus.
An initial inquiry by WorkSafe was now under way.
Auckland Transport (AT) media adviser James Ireland said staff were advised of the incident on Friday and had been told Ritchies Transport was undertaking a full investigation.
"Our deepest condolences go out to family and friends affected by this tragedy."
AT would assist in the investigation, and any other inquiries or investigations in any way it could, Ireland said.
"Our deepest condolences go out to family and friends affected by this tragedy."
Ritchies Transport has been approached for comment. The company operates more than 80 double-deckers.
Statistics released earlier this year by AT revealed Ritchies Transport had a disproportionate number of accidents compared with other Auckland operators.
While the company had 260 buses in Auckland, 19% the city total, it was responsible for 48% of accidents, 1 News reported.
