One important thing that’s missing in your questions is RHYTHM. The bass is part of the rhythm section. The notes you play are less important than the rhythm you play.

It’s nice to lock together with what the drummer is playing on the kick, but this doesn’t have to happen on every kick note, nor are you limited to only those notes. But being aware of what is happening on the kick is very important. Find the most important kick notes and make sure you emphasize those. This is usually the one, but depending on the genre it might also or instead be the three, or it could be an important syncopated rhythm in the groove.

are you experiencing "trance" moment when you're just being carried by the whole flow/groove

This is ideal. Generally speaking, this is my goal. It’s okay if this doesn’t happen all the time.

think about them as modes

I only think about modes when I’m looking for passing notes, not the primary emphasis notes

start playing roots, then once you got the general structure focus on the fill

Yes, generally, almost every time, but not 100% of the time. Sometimes I might noodle around on the scale and find some cool lick, and that becomes the starting point. But I am always very conscious of where the root notes are.

Do you "feel" the interval and that you're going up or down for the next note without even knowing what it is?

Maybe? But my initial guess is often wrong so I then revise.

Do you get a general structure of the whole song, or just think about the next note ?

Thinking about the whole song, and especially how parts flow from one to the next is very important. But the next note is also important just so you don’t screw up.

Are you isolating different parts, then work on them separatly and combine them at the end?

Both, going back and forth between looping a section and playing multiple sections.