That's because people that play bullet try to play their moves as fast as they can.
Bullet rating

It is faster to go up, and faster to come down, if you play bullet, especially 1/0 bullet.

I think there is a perception that it goes up and down faster because you are drawing from a larger sample of games. You can play 20 bullet games in the time it take you to finish a 15/10, so it seems like the swings are larger, even though they are likely comparable to the swings experienced over a similar number of games at a different time control.
Yeah, but the original question was about the distribution of elo in bullet rating system. It should be distributed the same way as blitz or rapid. Should not be?

Elo is supposed to be like percentile.
Yes, and notice that because of this only the distance between elements matters. The numbers representing the elements can be anything you want. In other words 1500 could represent the 50th percentile in one rating category and the 30th or 67th or whatever percentile in another category.

Yeah, but the original question was about the distribution of elo in bullet rating system. It should be distributed the same way as blitz or rapid. Should not be?
At the start of the website chess.com probably attempted to do this, but it will depend on the participants. For example imagine only GMs played bullet and only beginners played blitz. Then take 1 average person and have them get a rating in both bullet and blitz, what do you think will happen? Their blitz rating will be much higher.
In reality many people play both bullet and blitz, but beginners tend to dislike very fast time controls, and titled players tend to dislike long time controls. So in general faster time controls tend to be a little harder to get a higher rating because the participants are stronger on average.
But I think this is especially true at lower levels where players don't have much experience with bullet. My blitz and bullet ratings are pretty close. Maybe less than 100 points difference, but for a new player their bullet rating will probably be many 100s of points lower.
Thank you. That was helpful and clearly explained. I didnt realize that stronger players tend to play bullets and weaker players prefer blitz with longer time limits.
Also chance plays a bigger part in bullet then in other time controls (especially at lower levels) so that most players are closer to 50th percentile then in other controls. Which in theory means players whose rating is below the 50th percentile should have higher ratings then in blitz but I think like mentioned before those players rarely play and when they do they lose all games.
Some people are better at some time controls and not at others. For example I like blitz, bullet, and classical. I hate rapid.
I know lots of people who are higher in bullet than anything else. (sunaya1, Hikaru (I think), WFM AlexandraBotez, and others.). My blitz and bullet are about the same
You should not expect your numbers to be the same. Some people need more time to think while other people like flagging other people on time. It's no problem if there is a large rating difference: It just shows what time controls you are better at.
Bullet rating makes zero sense. Elo is supposed to be like percentile. Yet I have never encountered player with higher bullet rating than blitz rating on chess.com. Average is like 200-300 elo lower including myself, which makes zero sense.