"Does she work for you?", Mr Bloomberg is asked. "Beats me," he answers. "I hope not, cause she is not available if she does."
Well, it's good to know that Mr Bloomberg, newly single after a 20-year marriage, doesn't attempt to date his own employees. He oversees a huge empire, employing 2,000 journalists and support staff and supplying quality financial information around the globe.
Ask anyone at Reuters what they think of Bloomberg, and they have two answers. The first is for public consumption: "no serious competition." The other is whispered in private: "They are big and getting bigger."
And so they are. This year, with revenues of $1bn, Bloomberg will take over the second position in the financial information market, exceeding the market share of Dow Jones-Telerate. The company has grown at a rate of about 30 per cent a year since it was launched in 1981.
It has done so by paying good salaries but wringing every last drop from employees. There are no job titles at Bloomberg, and -- ostensibly -- no hierarchy. Nor, however, does he insist on taking absolute control. " I lend the name," he says. "That's the value. Look at Col Sanders -- people think he still cooks all that chicken, even though he has been dead for two years." The approach has given him an undoubted edge in the market for financial information, to which has been subsequently added the bells and whistles of a full-service news wire.
Still, Reuters is far bigger. Can Michael Bloomberg, the former broker and Harvard Business School graduate, really catch up? "We are a quarter of the size of Reuters, and you are asking if that gap can be bridged," Mr Bloomberg says. "Of course it can. Ten or fifteen years ago we didn't even exist."
His confidence is impressive, even alarming. It is easy enough to believe the stories about his departure from Salomon's, where he was shown the door because he had too many opinions about how the company should be run.
Mr Bloomberg saw a market for real-time information about stocks and bonds. His first efforts, helped by a intuitive understanding of Wall St. and insights into the world of computers and communication, were simple affairs. Today, however, the Bloomberg box, which sits on trading desks (and newsrooms) around the world, is sophisticated, supple and easy to use. He has since added books, magazines and even television.
But Mr Bloomberg is far from satisfied. At 54, he sees challenges ahead, not least the roll-out of Bloomberg Television into new markets. The service is already up and running in the US and was recently launched in France. Carefully customised for each home market, it is set for launch in the UK at the end of the year as part of Rupert Murdoch's digital satellite network, to be introduced in November by BSkyB.
So how profitable will the television business be? Mr Bloomberg is refreshingly blunt on the subject. "It's hard to see what you might call the media businesses generating anything like the money that the terminal business generates," he concedes. "We make $930m a year and are growing at 30 per cent. We'd have to be awfully successful at television to come close to that."
And he isn't even convinced that television is the best way to communicate information. "The market for serious news is small," he says. "The market for business news is a lot smaller than that, and the market for business news on a sequential access medium is tiny. TV and radio don't lend themselves very well to imparting selective information, so I'd rather go to the newspaper or to my terminal."
So why be in television at all? The answer is vintage Bloomberg, and a lesson to would-be entrepreneurs. "Our brand is better known now because we went into TV," he says. "The fourth estate [the press] loves to write about itself, so we get written about a lot more now that we are in the TV business.
"A cynic might say we are in TV to sell the main business [of terminals]. That's not quite true but its not wrong either. We wouldn't go in if it didn't sell terminals. We have a mens' room because we have to have one to sell terminals. But it doesn't earn any revenues."
Still, he insists that he will make a profit out of television, and wouldn't be investing the huge sums to develop the product if he didn't think it would make money.
Already rich beyond the dreams of avarice -- "I can't spent the money I have now," he says -- Bloomberg is still firmly committed to the business. In the future, he plans to roll out yet more TV services, and sell more Bloomberg terminals.
"I want to do it everywhere," he says. "Where there are capital markets and the need for news, we want to do it in the local language."
So what about all those rumours that he is prepared to sell? Merrill Lynch, the investment bank, has 30 per cent of the company, but the rest is Bloomberg's.