Bullet chess skills that you don't need in slow chess: good connection, good mouse, flagging skills (when/how to give check, how to premove, how to advantage of premoves, etc.), and very quick pattern recognition - you can be a lot slower in this regard in normal chess.
What's also important is that you don't care about making bad moves. You just need to keep moving, no matter what.
You should also have a decent opening system which you can play against almost anything, so you don't waste time in the opening.
And BTW, intuition you gain from *learning* about many many positions, such that you know exactly what to do when you see something similar on the board.
In fact, I'd say that calculation is more talent, since some people can't seem to calculate no matter how hard they try. Anyone can learn some intuition though.
I've noticed that I stink at bullet and my ratings go up considerably as the time control goes up, you can almost graph it as a straight line...guess I'm a calculator and not an intuitive player which is what I hear the bullet players are. Wonder if intuition is just something you have or don't have, kind of like IQ, which is mostly innate, or if you can develop chess intuition? I have been playing a long time and don't seem to be able to improve on short games....oh well, not going to obsess over ratings, I enjoy short games too much for that. Would like to hear what others think???