Bullet chess is to real chess as soda is to nutrition. Bullet chess to me seems like one of those video games where you try to shoot as many birds as you can in one minute. If you like bullet, then go ahead and enjoy it, but thinking that it is going to improve your chess skill is to me a fool's errand.
I think bullet chess creates incentives to make bad moves as long as they are fast moves. Because fast moves win, your chess mind gets into a rut where you have not really thought about the position in front of you and you keep making moves that do not fit the position. What you are doing is practicing over and over making bad moves.
Congratulations to you for appreciating the beauty of slower chess games.
1. I started playing 30 minute games, rather than so much bullet.
2. I stared playing daily chess (3 days per move)
3. I started working through Srokovski's Chess for Post Beginners. (On chapter 4 now)
4. I started doing tactics, maybe 50 a week.
I haven't devoted very much time to those 4 things, but my thinking has become a little deeper and I am more actively seeking (and sometimes finding) tactical opportunities. When I used to get a bullet opponent who was ranked 1250 or higher, I would pretty much figure I was going to get stomped. Now I am seeing their blunders and putting up a better fight. (Unfortunately my recent improvement at bullet incentivizes me to play more bullet, when it was by playing less bullet that I got better at it!)