How long did it take for you bullet players to be able to play at that pace ?

When chessplayers talk about intuition the mean feel for initiative or sense of danger. Chess is way too complex to do everything intuitively , it would destroy your subconcious mind and break you. Saying bullet is real chess is like saying a bar room brawl is like professional boxing, a brothel like real love or call of duty like war.

There are different kinds of bullet - the 'normal' case is that bullet is just the immediate instinct from slow chess, representing all the experience/intuition/chess vision from slow chess, and so in this case bullet skills broadly measures overall chess skill.

BUT....with 60 seconds for all moves mouse skills and hand-eye coordination also matter, and there are some bullet players with quite high ratings (~2200) who just play rubbish chess and try and rely on their ability to out-move the opponent on speed and run them out of time ('rubbish' here means some kind of totally passive e3-d3-g3 stodge which is positionally awful but can take a while to break down).

Bullet is rather poker like guessing premoves. A GM who contemplates 1-2s per move will lose most games to a premoving noob.

You wanna know how to get fast? See here: lichess.org/forum/general-chess-discussion/speed-has-replaced-quality-here-on-lichess-in-particular?page=1

Bonus question: u know which word was abbreviated to „Bullet“?

Sarg already answered it.

@Blindkingmen3 I guess i have a long way to go until i can read the board decently, i'm 1390 elo currently and have played for one year from scratch so i'm at that frustrating stage where i get caught frequently with traps and basic tactics (of which i'm trying to learn about).

Not sure i'm ready for bullet as yet but maybe i'll give it a go sometime soon.

I think it's easy to imagine why some GMs are weak in bullet - a 50/60 year old GM hasn't got the same physical reflexes as younger people however good their brain still is.

It's also not surprising that several of the people at the top of the bullet leaderboard (like Firouzja or Sarin) are at the age of best physical reactions.

So the loss of sarin to agadmator was a gift, like fide advertising him. Man he truly is the godfather having all in his pocket.

Anyhow in the book i read the strongest bullet player in soviet russian wasn't very strong compared to the others i think.

Is there a definition for bullet timers?

I believe 1/2 is bullet and 1/3 is blitz. Same for 2/1 and 2/2.

Nevermind:
"A variant of blitz chess, bullet chess games have less than three minutes per player, based on a 40-move game,[6][7] and this extends down to one-minute-per-player games;[8] ..."

I like fast games, and I like mostly learning by playing instead of ... however else you're ~supposed~ learn and/or play chess.

That said:
"Criticism

Many top chess players do not take rapid, blitz and bullet chess as seriously as chess with standard time controls. Some dismissive quotes from top chess players may serve to illustrate this:

"Rapid and blitz chess are first of all for enjoyment." — Magnus Carlsen[78]
"Playing rapid chess, one can lose the habit of concentrating for several hours in serious chess. That is why, if a player has big aims, he should limit his rapid play in favour of serious chess." — Vladimir Kramnik[79]
"Yes, I have played a blitz game once. It was on a train, in 1929." — Mikhail Botvinnik[79]
"He who analyses blitz is stupid." — Rashid Nezhmetdinov[79]
"Blitz chess kills your ideas." — Bobby Fischer[79]
"To be honest, I consider [bullet chess] a bit moronic, and therefore I never play it." — Vladimir Kramnik[80]
"Blitz – it's just a pleasure." — Vladimir Kramnik[81]
"I play way too much blitz chess. It rots the brain just as surely as alcohol." — Nigel Short[82]
"Blitz is simply a waste of time." — Vladimir Malakhov[83]
"[Blitz] is just getting positions where you can move fast. I mean, it's not chess." — Hikaru Nakamura[84]"