FRESH HONEY Caruso-Cabrera, Bartiromo (inset, left), Parr (inset, right) Is Michelle Caruso-Cabrera trying to become the new "Money Honey" on CNBC? Rumor has it, she's torn a page out of fellow so-called anchor babe Maria Bartiromo's play book, covering the $30 billion Bear Stearns bailout while allegedly dating the man who orchestrated it, Gary Parr. He's the deputy chairman of Lazard Frères & Co., a 50-year-old divorced dad of two who devised the plan to funnel $30 million of Fed-backed money into the tanking bank, the fifth largest on Wall Street. He's the guy Bear Stearns CEO Alan Schwartz desperately dialed as he learned of the investor run on the Wall Street behemoth. He's also a big investor in indie films, having backed Proof and At Home at the End of the World, and he's known for wining and dining journos at premieres. But, rumor has it, Caruso-Cabrera is his favorite.