Quite simple, don't play bullet until you improve your overall understanding of the game.
Help! I can't get past 800 in bullet! Any tips?

You will hit a limit, specially if your rating is low to start with. That's because there is limited feedback on bad play in bullet. You can play terribly and still win half the games and think you're doing great, but you're rating will not go beyond a certain point because you're always playing terribly against other players who do likewise.
Once you developed a certain competence, then I agree: you can improve in one time control by playing a faster one, because when you go back (for example, from bullet to blitz), you realize you have plenty of time.
Title