Most coaches tell their students at your level NOT to play bullet. It will just teach bad habits that will interfere your development.
I will have to agree with this statement. "First improve overall chess skills then try to play bullet afterwards", sounds very real.
Something like "15I10 rapid" be a good idea before embarking on bullet.
The best way to become a better bullet player is to become a better chessplayer.
if I were your coach, I would have you stop playing bullet and blitz. Learn basic principles of openings and endings. And when you are a legitimate OTB 1700+ player, then go back to faster time controls.
Most coaches tell their students at your level NOT to play bullet. It will just teach bad habits that will interfere your development.