NEW YORK — You might have seen an affable, 6-foot-5-inch older fellow pacing the paths of Central Park recently, talking to himself. Well, that was no ordinary man. Among his accomplishments: a Rhodes scholarship, a flawless jump shot, even a seat in the Senate. And of late — surprisingly — a moment in the footlights.

Yes, Bill Bradley decided the new world he wanted to conquer, after distinguished careers as a New York Knick and a U.S. senator, was that of a storyteller onstage, such as Mark Twain. And that is how “Rolling Along” came to be, and why Bradley made mumbling loops around the park, the way he used to spend hours by himself, practicing layups. Only now, he was practicing his lines.

“Rolling Along” is the show he’d written over the past several years about his extraordinary life, going back to his days as a gangly basketball wunderkind from Missouri, on his way to Princeton and the Olympics. Before the coronavirus pandemic began, he recited it, script in front of him, before small audiences in 20 cities. Last December, he did it again, but this time from memory, for four nights in a theater on West 42nd Street. There, in the room with an audience and five cameras, documentarian Michael Tollin (“The Last Dance,” “Hank Aaron: Chasing the Dream”) put it on film.

“Rolling Along” had its premiere on June 16 at the Tribeca Film Festival — a 90-minute movie as unvarnished as a weathered porch on the Mississippi, the river that inspired the film’s title. It’s just Bradley onstage with a chair, table and glass of water, candidly recounting his biography, a guy seemingly at ease and eager to explore this new terrain as a public figure. In an interview, he confesses as much, about why he made the show: part of a lifelong quest, he says, to “belong.”

“It’s me as an only child,” Bradley declares, “wanting to give myself to a larger family.”

All politicians are performers of one sort or another, the lucky ones by dint of natural gifts. Others lean heavily on the skills of speechwriters. Still others just seem to be (too) in love with the sound of their own voices. You can see in “Rolling Along” that Bradley falls into another, rarer category, one defined by a need to pull himself off the pedestal, to express his feelings in lyrical musings, to reveal a vulnerability underlying his achievements.

“My hope was that people will feel a connection because of the humanity of the piece, and in elements of it people will see their own life,” Bradley says in an interview.

One person who felt a connection was filmmaker Spike Lee, a Knicks fan of rabid dimension, who’s been friends with Bradley for years. Running into each other before the pandemic at Clyde Frazier’s Wine and Dine, the now-closed Manhattan restaurant of another ex-Knick, Walt Frazier, Bradley told Lee: “I’d like to do this thing for you to get your opinion.” Lee invited him to his Brooklyn office, where Bradley read to him “Rolling Along.”

“At the end, he has tears in his eyes,” Bradley says. “And I think, ‘Oh, whoa, that’s confident confirmation of something.’”

Lee, too, recalls waterworks. “A couple of scenes, my eyes were welling up,” he says in a phone interview. “Those are my guys, ‘69-’70,” he adds, about the NBA championship team Bradley and Frazier were both part of. So smitten was Lee by Bradley’s performance that he would sign on as executive producer of the documentary, which is still in search of a distributor.

Bradley, who turns 80 on July 28, has always had intellectual leanings (though in “Rolling Along” he claims to have struggled academically when he began at Princeton). He’s written six books and enjoys a wide circle of culturally enlightened friends, including Emanuel “Manny” Azenberg, longtime producer of Neil Simon’s plays on Broadway.

It was Azenberg who first encouraged Bradley to try his hand at the stage, after hearing Bradley tell anecdotes at a reception. Azenberg even gave Bradley the name of a stage director, Daniel J. Sullivan (most recently, Broadway’s “Summer, 1976” with Laura Linney and Jessica Hecht), who offered the ex-New Jersey senator some tips over the phone.

As “Rolling Along” clearly records, Bradley was not born to be an actor: His gestures are halting and his voice is all up in his head, rather than from his chest. But it’s of no matter. In fact, that’s kind of the charm — a warmth intensified by his candor and sincerity. It’s surprising to learn, for instance, that as a young man he was a devout evangelical Christian, a faith that pegged him as exotic at an Ivy League college. (He became estranged from the religion, he reports, while he was at Oxford on the Rhodes scholarship.)

The memory feeds a theme that Bradley returns to again and again about never quite feeling he fit in — the boos that sometimes greeted him in Madison Square Garden in 1967, his rookie season with the Knicks, still sting. (Soon after, any disappointment with his court performance evaporated, and New York fans embraced “Dollar Bill” Bradley — a nickname bestowed on him because of his perceived thriftiness by team center Willis Reed.) No doubt, too, as a White athlete who had witnessed discrimination against Black teammates starting with his playing days in Missouri, a sensitivity to the marginalization of others was instilled.

So maybe it isn’t surprising that Bradley wanted to revisit acceptance on another stage. “I kind of like when the audience is with you. You know, when I ran for president,” he says, of his unsuccessful Democratic primary run in 2000, “there was the phenomenon of walking into a room of 90 people in Iowa or New Hampshire or wherever, and your job was to convince the 90 people that you’re the guy.

“And what I would do, I tried to connect to the eyes of the people in the audience. Connection to the eyes was part of the performance in politics in a small setting. You couldn’t connect to the eyes in Madison Square Garden. But you could connect to the eyes in this kind of intimate campaigning of under 100 people in a room in Iowa, New Hampshire, South Carolina.”

This desire for bonding drew in Tollin, the film’s director, too. In 2019, he was invited by a TV producer friend in Los Angeles to hear Bradley read his play in, of all places, the commissary at Warner Bros. studios. “There’s Bill Bradley at a table with a stack of papers,” Tollin marvels, noting that his previous encounter with Bradley was when he made an appearance on an episode of “Arliss” directed by Tollin. (The HBO series was about a sports agent played by Robert Wuhl.)

Tollin told Bradley afterward that “to me, this is a play that would work really well in regional theaters,” and after sending him “four pages of notes,” the director found himself in Bradley’s office at Allen & Co., the New York investment firm he joined in 2001. “Then COVID killed it and we pivoted” to film, Tollin added.

“Rolling Along” briefly addresses the end of Bradley’s long marriage to Ernestine Schlant, a college professor, which produced a daughter, Theresa Anne. But some of the piece’s most moving passages have to do with the lessons Bradley learned during his childhood in Crystal City, Mo., a town of a few thousand people outside St. Louis, where his father was the local banker and his mother drove him and several Black teammates to their Little League baseball games.

Repeating a key anecdote from the monodrama, he tells me about the time they drove to a tournament in Joplin, and many of the hamburger joints and local hotels wouldn’t allow in the Black players. So they all stayed in a fleabag hotel. “The guy who ran the team didn’t move the White players to a better place,” Bradley recounts. “He said, ‘We stay together as a team.’”