"How have you changed over the last 15 years of playing out here every day?" Bradley asked.
"Oh man, a lot. I mean, I'm calmer. When I was young I was always excited, you know? Got to do it today, and I was always paranoid about not ever being able to play good enough, you know," Marsalis replied.
"I'm gonna ask you the same question that our friend Ed Bradley asked you 15 years ago. How's your playing changed in the years since?" Safer asked.
"I think just a natural wisdom that comes with age. Mostly, I think I have a different type of weight in my sound. In just the 15 years I know more music. So when I'm playing I feel like it reflects a deeper knowledge. I think I hear better too," Marsalis replied.
Their mission - his and the band's - is to keep jazz alive, writing new music and paying homage to the treasures of the past.
Like Marsalis, most of his Lincoln Center musicians were classically trained, equally at home with Bach and the blues. They come from big cities and small towns, and include youngsters like pianist Dan Nimmer, 28, and veterans like Joe Temperley, an 81-year-old Scotsman.
"When you play in a big band, you sacrifice a lot. We have some of the greatest soloists. They know they're gonna play one solo a night. It's a tremendous sacrifice," Marsalis said.
One night, you'll find them at New York's historic Apollo Theater, playing the score for a silent movie about trumpeter Louis Armstrong. The next night, who knows?
"We've played everywhere from prisons to parks, picnics, old folks homes and nursery schools. On the subway," Marsalis said. "I spend more time on the road than at home. I love to be in a different place."
But he told Safer he is afraid of flying, which makes things more difficult.
"But you travel across this country…by car. You won't get on a plane," Safer remarked.
"I love it, too," Marsalis said, referring to the road trips. "I get to stop at people's homes. I get to get good meals. I get to connect with all the people I've known."
He took to the car after a white-knuckle flight years ago. Traveling overseas though, he has no choice but to bite the bullet and fly.
"I don't really have to steel myself. Especially if I'm with my guys, then they're teasing me the whole time. So I have to…act like I'm not afraid of it. But some of the ones that are teasing me are afraid, too. So we're all acting," he told Safer.
Wherever they travel, Marsalis and company are hailed as America's best. And local music royalty, like rocker Eric Clapton in London, come to pay their respects.
Chatting in the shadow of the Tower Bridge, Marsalis says that for all his renown and decades of experience, his baby face gets in the way.
Like an incident he had when he walked into a bar: "And the young lady said, 'Well, sir, we've got to see some ID.' So I'm laughin, I'm sayin' 'My sons, they're old enough to drink.' I'm like, 'These are my kids.' And she says 'Well, I can't, I've got to see some ID, sir.' And they just shake their heads and say, 'Boy,'" Marsalis said.
He is a walking encyclopedia of jazz history, the legends and their music.
The London concerts focus on jazz giants of the past, their work a revelation to listeners who seldom experience the power of a big band at full throttle.
There's music from the 1920s by the deliciously named Jelly Roll Morton. "Raconteur. Pool shark. The first great composer of jazz," Marsalis said.