As CBS News Sunday Morning Correspondent Rita Braver reports, Bradley's having a blast. And he can afford to have fun because he's the only Democrat challenging Vice President Al Gore for the presidential nomination.
She recently caught up with him along the banks of the Mississippi River in an effort to determine how he plans to take on a candidate who is the heir to an administration that has presided over an economic boom.
"I'm having the time of my life," he says. "I should be paying people for this experience. People say, 'What's the difference between your campaign and the vice president's?' And I say, 'I'm having fun.'"
"Every election is about the future and not about the past," Bradley continues. "And my answer is, 'We get more people on the train of prosperity. We cover people with health insurance. We reduce the number of children in poverty. We make good on the promise of America to more Americans.'"
So far, Bradley has sidestepped controversy by holding back specifics of how he'd deal with those issues until the fall. His strategy for now is to connect with voters, almost one by one, in Iowa and New Hampshire.
Bradley has announced detailed proposals on a few key issues, however. He says he's in favor of registering all handguns, and he supports funding for ethanol production from grain, which he was opposed to in the Senate.
First and foremost, he talks about campaign finance reform and banning some types of contributions.
"We all know we live in a country, where it's supposed to be one person, one vote, but we know that people who have money have more clout than one vote," he says.
But even as Bradley is making campaign finance reform one of his trademarks, he's still had to raise big bucks to stay in the race, and one place he's scored is far from the cornfields of Iowa.
In Hollywood, Bill Clinton may get star treatment, but Al Gore doesn't have quite the same box office appeal. So Bradley has gained backing and money from the likes of Harrison Ford, Spike Lee, Sting, Dustin Hoffman and actor/director Sydney Pollack.
"I supported Clinton, but I didn't go out and make phone calls or anything like I'm doing now," says Pollack. "An awful lot of my friends who are doing this now are people who have never, never gotten involved politically before, but who sense something new and off the beaten track with Bradley."
Democratic political consultant Harrison Hickman says Bradley's Hollywood connection can help him build momentum.
"The advantage of Hollywood money or any kind of celebrity money is that it gives a certain cachet to the campaign and says to other potential givers, 'Hee's someone worth looking at; here's somebody worth giving my money to,'" says Hickman.
Of course Bradley's years as a basketball superstar make him a celebrity in his own right, and old NBA pals like Phil Jackson and Walt Frazier helped him collect $500,000 at just one Chicago fund-raiser.
So far, he's raised $11.7 million to Gore's $19.5 million, and the fact that Bradley has done so well has helped create the perception that he's a serious contender and has made the Gore camp edgy.
Bradley graduated from Princeton University, where he was an All-American and went on to become a Rhodes scholar. He served 18 years as a United States senator from New Jersey, and later did a stint as a CBS News commentator.
He likes to come on as an outsider, however, and is still close to his roots in the small Missouri town of Crystal City. This is one of the major distinctions he draws between himself and Vice President Al Gore, who spent much of his youth in Washington.
Thus far Bradley won't jab at another one of Gore's weak spots. "I think that he's been a very loyal vice president. I think that he's been there through good times and bad times, so let's leave it at that," he says.
But there's no question that Bradley's attracting many ABG voters who think "anybody but Gore" should get the nomination.
The Gore campaign, however, points out that most polls still show Bradley behind by double digits. Bradley must build a broader base. But on many major issues, there is little difference between the two candidates.
Senator Bob Torricelli
"Somehow the confidence Bill has and the integrity, his range on issues has to be communicated," says New Jersey Senator Bob Torricelli.
"It doesn't mean anything unless you can get it across to people, Torricelli says. "It's not easy. He didn't do it as senator; he has to do it to become president."
But Bradley is content to play it low key. He likes to brag about his wife Ernestine, a German-born college professor he calls his best friend. Their 23-year-old daughter has stayed mostly in the background, though the small family was rocked recently by Ernestine's successful battle with breast cancer.
"It reminded me of how life is very fragile," says Bradley. "What you think will last forever can disappear tomorrow.
"That means you have to live it every day," Bradley says. "That means you have to express what you have in your heart. You don't hold it back for any other time. I think that was the biggest lesson."
Bradley says he decided that this was his time to try to capture the presiency, but Torricelli says it may be a rough ride.
"To defeat an incumbent vice president when the nation is at peace and [during] prosperous times after a successful administration, it would not only be unusual, it would be unprecedented," says Torricelli.
"But you know, a guy from a small town in Missouri, who can't shoot, can't jump, and can't run making it to the world championship New York Knicks - his odds are better in this one," he adds.
So in these early days of the campaign Bradley concentrates on setting a tone and staging an upset.