The 95-year-old monarch held an audience with the head of the financial institution the day after she knighted her top royal physician, Professor Sir Huw Thomas, during a personal investiture.
The Queen was pictured with Mr Bailey, one of a number of national figures the head of state meets during the course of the year, at Windsor Castle.
Concern for the health of the Queen has been heightened in recent weeks after she pulled out of a number of major engagements, spent a night in hospital and was ordered to rest by royal doctors.
It is likely to have been Prof Sir Huw who advised the head of state to take things easy after she underwent preliminary tests in King Edward VII’s Hospital on October 20.
The Queen has been carrying out light duties since then, but also sprained her back, leading to her missing the Remembrance Sunday service.