They didn’t need to buy off Bloomberg, he is a left wing nanny state fanatic. He is also terribly jealous of Trump being the most famous billionaire from NYC. For Bloomberg it is all “what about Meeeee?????”
N.Y. state is VERY much in play! Trump has much of the state and even parts of NYC, in his pocket. Even Harlem, which IS in Manhattan, is good for The Donald!
Trump probably doesn't get Brooklyn, I have NO idea about Queens, since many parts are now Asian and Hispanic, or the Bronx.
OTOH......Staten Island is almost 100% for Trump.