Bloomberg himself said pre-2008 that he'd only consider running if the race were between someone like Huckabee on the Republican side and Obama or Edwards on the Democratic side.
What if the 2008 election had been Mike Bloomberg running against Barack Obama and Mike Huckabee?
Who is Bloomberg's running mate? David Boren, Sam Nunn, and Chuck Hagel were the three folks considered most likely to be the running mate. Bloomberg's base is a mix of Clinton-leaning Democrats, socially moderate republicans, and hawkish democrats.