"He was taking handwritten notes in this vast, leather-bound notebook of his that just grew and grew and grew," Gun says of those meetings, which went on for five days. "I could tell it was something that he took seriously."
The end result, Official Secrets, stars Keira Knightley as Gun and Matt Smith as Bright.
The movie depicts the decision Gun made in 2003, while working for British intelligence agency GCHQ, to leak a secret memo exposing plans by the American government to blackmail members of the UN Security Council into backing the Iraq War.
Directed and with the script co-written by Hood, Official Secrets generates tension by dramatising real-life events. But the methodical espionage thriller avoids taking substantial liberties with the true story.
Although a previous version of the script consolidated two of Bright's key colleagues at the Observer newspaper into one composite character, Hood's film honours their contributions by restoring Peter Beaumont and Ed Vulliamy as individual characters (played by Matthew Goode and Rhys Ifans, respectively).
"I thought the credibility of the movie would suffer if I took licence with significant people and events," Hood says. "It's not like we're doing something from 500 years ago. These people are alive, and they'll say, 'Not so'."
Loyalty to the actual events also meant embracing an unconventional plot. The storyline involving Bright and his journalistic cohorts, for example, takes a back seat in the final act. At that point, the narrative shifts to the defence crafted by Gun's lawyer, Ben Emmerson (Ralph Fiennes), after she is charged with breaking Britain's Official Secrets Act.
"It doesn't fit a traditional structure," Hood says, "but I hope I'll be forgiven for that because that is true to what happened."
Official Secrets probes myriad issues that remain resonant a decade and a half later, including government overreach and accountability, the toxicity of anti-Muslim sentiment, and the merits of an intrepid free press.
But Gun's personal story proves to be the prism through which the film investigates such sprawling topics.
When Bright saw the movie for the first time, he was struck by how Gun was the figure on screen he most identified with. ("And I'm a character in the film!" he says.)
By positioning Gun as an everywoman, Official Secrets asks its audience to ponder the moral dilemma at its core.
"I didn't set out to be a whistleblower," Gun says.
"Hopefully people will see it and come away with the thought, 'What would I do if I was in a similar situation?'"
•Official Secrets opens in New Zealand in November.