Take my advice with a grain of salt because I am terrible at bullet (although to be fair, I almost never play it), but I do play a decent amount of blitz. My advice is to slow down and play longer time controls; paradoxical sounding, right? The best bullet/blitz players in the world are also the best long time control players. It has to do with pattern recognition. They identify patterns almost instinctively, so they barely need to "think" in a fast-paced game. If you can learn thematic motifs and tactical shots by whim, then you will play fast games more accurately then just trying to move faster with little insight of the position.
In short, improve long time controls and pattern recognition to become better at fast games. Also, opening theory helps because then you can play the opening super quick and have a few more precious seconds to think later in the game.
Fellow chess players help me play faster in bullet.