The 87-year-old actor made her debut as 007's chief M in 1995 film GoldenEye at the same time as Brosnan appeared for the first time as the spy hero.
Dame Judi told Louis Theroux on his new BBC show: “I hope Pierce wouldn’t mind me saying, but we were both very frightened, suddenly taking over those two roles, it was very demanding and one was nervous about it.”
The star of stage and screen revealed she was persuaded to take on the role by her late husband Michael Williams.
She recalled he told her: "You’ve got to do it, I’ve got to live with a Bond woman."
Williams died in 2001 after battling lung cancer.
Theroux asked Dame Judi: "Are you OK talking about how it came to an end, how he came to die?"
She replied tearfully: "Well he wasn't well... I'm not good at it, actually."
"Yes, he died in 2001 of lung cancer. Smoking you see, all that smoking when we were young.
"I was in New York and they said he was not well. My agent flew out and we came back on Concorde the next day and it aborted take-off.
"We got off and we went back and said: 'Oh, it'll be alright.' We got on another plane and the same thing happened. It was a long old time to get back.
"We got back here and we were all in the house together and that was very, very good indeed."
Watch: Louis Theroux Interviews Judi Dench for his new BBC series