Michael Bloomberg may be the best-connected man in New York. He knows everyone. Watch him in his Paul Stuart tuxedo, red bow tie, and black tasseled loafers as he walks through a room at a Park Avenue social event -- the Citizens Committee for New York City awards at the Waldorf two months ago, for example. He is mobbed from the moment he enters the room. Arnold Scaasi wants a handshake; Ruth Messinger whispers in his ear; Kofi Annan poses with him for a photo op. Stepping to the podium to accept the Brooke Astor Award for Philanthropy, Bloomberg, the son of a bookkeeper from Medford, Massachusetts, can't resist making a teasing reference to his modest Jewish heritage compared with the high Wasp quotient of the crowd, pointing to the socially connected Schuyler Chapin and saying, "Only someone named Chapin, not Bloomberg, could wear a green dinner jacket."

Bloomberg hasn't brought a date, and he has been unattached since breaking up with his girlfriend of several years, Mary Jane Salk, a writer and the widow of noted child psychologist Lee Salk. "He has been discovered socially in the past year," says Barbara Walters. "He's straight, intelligent, and attractive." These days, however, he seems unwilling to bring even casual dates to public events for fear of subjecting the women to untoward press scrutiny. Bloomberg was divorced in 1993 from Sue Brown, an Englishwoman who briefly worked as a secretary in Salomon Brothers' London office; he has two daughters, Emma, a senior at Princeton, and Georgina, a high-school senior and an avid horsewoman who competes on the show circuit. Dubbed the "anti-bimbo billionaire" by the New York Post for gallantly dating women over 50, he insists that he's got no problem with the older-man- younger-women thing; it's just that "I have more in common with women who are roughly my age." By all accounts, he seems to make a point of staying on good terms with the women in his life. "He's a great friend," says Christy Ferer, a now-married TV reporter who dated him in the mid-nineties. "He's fun, he's easy company. He's the Horatio Alger of Park Avenue."

He seems genuinely thrilled to be treated as a serious mover and shaker in New York. "I still pinch myself," he says without a hint of his usual sarcasm. "I'm amazed to be in these rooms. When I went to Harvard Business School, I was excited just to meet the sons of famous men." Now everyone wants to meet him, which is sweet revenge for a man fired twenty years ago from Salomon Brothers. Bloomberg-mania reached its peak in early March on the night of the Inner Circle dinner at the Hilton, where his table, which he shared with Democratic all-star guests like Ed Koch, Charlie Rangel, and Carl McCall, was so surrounded by journalists and well-wishers that the waiters had trouble getting through to clear the plates. After Rudy Giuliani's annual cross-dressing appearance onstage in stockings and heels, Bloomberg boasted that he had no qualms about filling the mayor's shoes: "I have great legs."

Convinced that Bloomberg is their best hope to retain New York City as GOP territory, Governor Pataki, state GOP chairman Alexander Treadwell, and State Senate majority leader Joe Bruno have publicly been falling over one another in recent weeks to embrace Bloomberg's self-financed candidacy, even though the billionaire was a staunch Democrat until re-registering as a Republican last fall. "I think Michael would be an excellent mayor and a tremendous candidate," says Pataki, insisting that Bloomberg's late-in-life conversion doesn't trouble him. "Ronald Reagan was a Democrat, too. It doesn't matter what you were or who you voted for twenty years ago." (Twenty years ago? Bloomberg was donating money to Democratic candidates just last year.)

"I like his cocky style," says Tom Brokaw, "but I'm not sure why he wants to do this. It's going to be much harder than he believes."

Bloomberg freely admits that he changed his registration merely to avoid the already-crowded Democratic primary. "I knew I couldn't do it as a Democrat," he says. "The party always protects its officeholders, and an outsider can't come in as a challenger." Bloomberg expects to campaign on the traditional Democratic side of issues: He's pro-choice, pro-gun-control, and, to a limited extent, anti-death-penalty. "I have no moral problems with the death penalty," he explains, "but I'm against it for practical reasons, because you cannot guarantee the state won't make a mistake." He wants to maintain the Rudy legacy of safer streets but would emphasize better community relations and a less-trigger-happy, more racially tolerant police force. "You're not going to find much difference between any of the other four and me," he says.

His message to the city's Democratic voters, who outnumber Republicans five to one, seems to be: If you could vote twice for Rudy, a real Republican, it'll be even less of a stretch to vote for me, a pseudo-Republican. "I like Mike, he's a friend, but I don't think it's doable," says state comptroller Carl McCall, who has endorsed Bronx borough president Fernando Ferrer for mayor. Consultant Hank Sheinkopf tried to talk Bloomberg out of changing parties and is working now for Mark Green. He gives a hint of the campaign to come when he says of the media mogul's GOP reincarnation: "It makes it sound like he has no principles."

Bloomberg, who recently stepped down as chairman of his company (though he retains the CEO title), has been preparing for the race by boning up on city policy in his own unique way: He's been visiting many of the local do-good projects -- a drug-treatment program, a home for the mentally ill -- that he's written checks to in the past. ("It gives me access," he says.) He commissioned Ester Fuchs, director of Columbia University's Center for Urban Research and Policy, to prepare an 1,800-page primer for him on local issues, from education to police to housing. "He doesn't assume he has all the answers and knows everything," she says. "He's trying to learn."

Bloomberg is convinced he's got what it takes to connect with the proverbial housewife in Queens. He's always besieged by people who want something -- a job, advice, money to invest in their companies, a charitable donation -- and his style is to listen patiently, an interested smile on his face. His pockets are usually full of business cards pressed into his hand by importunate strangers. "You have to listen," he told me at a Washington reception just after being cornered at the buffet table at midnight by a man eager to talk up his satellite company. "You never know. And I make sure everyone gets a response. People are so surprised and grateful, even if the answer is no."

Bloomberg travels with a posse of staff people -- press rep Christine Taylor, philanthropic exec and Koch alumna Patti Harris, and Washington government-affairs rep Kevin Sheekey, a former Moynihan aide -- but their role is to hang on the fringes until summoned rather than to run interference for the boss.

His company was built on a near-maniacal obsession with customer service: Each of his 156,000 data terminals worldwide sports a top-of-the-screen message urging clients to personally zap him an e-mail if they have a problem. Bloomberg is already kicking around the idea -- if he becomes mayor -- of establishing the equivalent of a 911 number for citizen complaints, which people can call to report a pothole or a garbage problem and have their calls directed to the right agency, with a 24-hour response time.

"New York has never had a CEO run the city," says Harold Doley, a black stockbroker and former Reagan-administration ambassador, who, as an informal campaign adviser, has arranged for Bloomberg to meet the Reverend Al Sharpton and other black city leaders. "As the stock market declines and city revenues taper off, Mike as a businessman is the ideal leader."