As far as I'm aware anecdotally (I interned at Bloomberg last summer) Mike was in a position that required managing technology in his previous financial job before starting Bloomberg itself. Perhaps a more useful skill than being a developer himself considering he had a few million of capital to hire his own team from the off!
Well, NYC finance is still about dealmaking, even in the days of digital trading. Business is still done face-to-face, and the sheer density of New York will probably make sure that deal makers are more valuable than technologists for the foreseeable future. That's not to discount technologists in NY at all, though (they're deal makers too). It's just the reality that handshakes and coffee are irreplaceable.
Speaking of coffee, a lot of his early deals were based on him going around to Merrill Lynch and buying people there coffee, then coming back later saying "I'm Michael Bloomberg. I bought you a coffee. Can we talk?"