Bigelow was a painter before she was a filmmaker and is still something of a recluse. But now she spends a lot of her time walking the red carpet.
"The Hurt Locker" has already won just about every major critics' award, plus Film of the Year from the Producers Guild and Best Director award from the Directors Guild. If she wins the big one, she'll be the first woman ever to win an Oscar for directing.
Critics say that Bigelow's "The Hurt Locker" is the best war movie made in years, and there's an irony in the fact that it's up against James Cameron's movie, Avatar.
"How sweet is this to be head to head with your ex husband? Incredible that the two films were made by people who were married to each other," Stahl asked.
"You couldn't have scripted it," Bigelow replied, laughing.
"There's this whole thing that's going on where people love to, they love to create a headline: 'Battle of the exes,' you know, 'War of the roses.' We were married two decades ago for a brief period of time and we've been friends and collaborators since," Cameron said.
As we talked about this with Bigelow at a ranch where she escapes from the hoopla of Hollywood, she said she and Cameron are now such good friends they swapped scripts and early versions of each other's movies.
"When he saw 'Hurt Locker,' did he say, 'You ought to do this, you ought to do that'?" Stahl asked.
"He said 'cut negative,'" Bigelow said. "Cut negative means you're done editing."
"Cut negative means it's perfect?" Stahl asked.
"It was a big compliment," Bigelow explained.
And now her little movie has as many Oscar nominations at Cameron's blockbuster, nine for both.
"I was stunned, shocked, thrilled beyond belief," Bigelow said.
Nominations include best actor, best screenplay, best picture and best director.
In "The Hurt Locker" - a riveting two hours filled with fear and violence - Bigelow shows how terrifying it is for a bomb squad in Iraq.
By using wobbly hand-held cameras, Bigelow heightens the tension and the sense of immediacy: she wants the audience to feel like the fourth member of the bomb squad.
"The ground just erupts, out of nowhere. I mean, it's just an incredibly harrowing, dangerous, volatile environment," she told Stahl.
She sees the film both as anti-war, and as a tribute to the soldiers who sign up to do this kind of work.
"These are men and women who volunteer, who are there by choice, who are walking toward what you and I and perhaps the rest of the world would run from. And they arguably have the most dangerous job in the world, yet they're there by choice," she explained.
"They don't know where to look. They don't know," Stahl remarked.
"You don't know where to look. It's an invisible enemy. And you don't know if the man on the third floor balcony is shaking out a rug or calling in a sniper strike," Bigelow said.
But beneath all the action is a film about the psyche of soldiers under siege. Bigelow opens the movie with a quote: "The rush of battle is often a potent and lethal addiction, for war is a drug."
"But it's also a sense of meaning and purpose that nothing else in your life can replicate, except the battlefield," Bigelow explained.
Her main character, Sergeant Will James, can only function when his life is in danger. He's a go-it-alone cowboy who breaks the rules and terrifies his squad members with reckless behavior.