Of all the politicians I’ve known over the years, probably none was more private or less eager to entertain than Bill Bradley. So I was surprised to hear that Bradley, at the age of 78, had undertaken to write and perform a one-man show about his life.

This week, Bradley has been previewing his “oral memoir” for friends in a theater on 42nd Street in New York, which is where I saw it.

His performance is funny, intimate and sometimes heartbreaking — not least for what it says about how Americans choose our leaders, and how we in the media cover them.

For those of you who may not remember, Bradley, a basketball legend and three-term senator from New Jersey, took on Al Gore for the Democratic presidential nomination in 2000. Because Gore was the sitting vice president, his campaign attracted the more experienced reporters.

Most of us assigned to cover Bradley, on the other hand, were kids on our first presidential adventure. (My wife and I met on the bus in New Hampshire; another reporter and a press aide on board would also fall in love and marry. It was that kind of campaign.)

We wanted Bradley to talk about the things that we thought interested voters — his upbringing, his marriage, his religion. These “character” issues were supposed to tell us who he really was.

Bradley was unfailingly gracious but maddeningly reticent.

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John McCain would sit in the back of his bus — the “Straight Talk Express” — and tell you anything you wanted to know about life as a war hero and party apostate. Bradley deflected; the first time I interviewed him, he pretended to fall asleep.

We found Bradley cerebral and remote, ill-suited for the modern presidency. He found us, I think it’s fair to say, fundamentally unserious.

But now here is Bradley, decades later, roaming a stage for two hours with nothing but a stool and a glass of water, telling us his story at last, apparently because he has been looking back and taking stock.

He poignantly describes the love of his mother for her only child and talks about his conversion to evangelical Christianity and eventual disillusionment. He describes the botched abortion of a woman he impregnated in the 1960s.

There’s the story of how he earned the trust of his Black teammates on the New York Knicks, in the years that Bradley says were the only ones in his life when he truly knew where he belonged. There’s a moving portrait of his years as a single parent in the Senate while his wife was teaching in New Jersey.

It turns out Bradley wasn’t really so uncomfortable with self-reflection. He carried a set of deeply personal experiences and insights, some of them searingly painful, that could have had every talking head in the country blabbering on for months.

It’s just that he didn’t think a presidential campaign should be about his personality and his inner life, so much as about his plans for the country.

He talked every day back then about the landmark tax reform law he’d written and his plan to rid politics of corrosive corporate money. We reacted as if he were reciting the “Epic of Gilgamesh” — in the original Akkadian.

Bradley understood the power of celebrity as well as any man or woman in Washington, but he stubbornly resisted the celebritization of our politics. In this way, he reminds me of another politician I’ve written quite a bit about, Gary Hart, who once cautioned a frenzied press corps: “In public life, some things may be interesting, but that doesn’t necessarily mean they’re important.”

If you look at what has transpired in the decades since, it’s hard to conclude that Bradley’s instinct was wrong. Personalities have overwhelmed parties; personal narratives have eclipsed ideology. Candidates share every aspect of their lives on social media, but, generally speaking, what they know about policy could barely fill a tweet.

What Bradley understood is that wisdom and narcissism can’t coexist. The more you obsess about yourself, the less you’re learning about everyone else.

I think now that Bradley would have made at least a fine president — maybe a very good one. Like the current occupant of the office, he would have gotten up every morning and quietly, methodically tried to do what was right.

But when I look at Joe Biden’s anemic approval ratings, I can’t help but think that’s not really what we want from a president now. I suspect some large segment of the public has grown so used to being entertained, or inspired by some kind of cinematic personal narrative, that they see it as intrinsic to the job.

When Bill Bradley walked away from politics almost 22 years ago, I figured he mostly had himself to blame. As I watched him leave the stage in Manhattan this week, I had to wonder how much of the failure was ours.