Now, it's not clear to me what he means by "master"
let's say I repeat three bars 7 times and after this seven repeats I can play those bars without errors and by heart; can be this considered mastered or do I need also it to be "full speed"
Using this approach I've noticed that I can learn by heart without errors 10 bars circa after just seven repeats
Yet even if I can "master" 10 bars after seven repeats, 10 bars is probably a chunk to large to practice?
Any thought?
1. Can you play the passage at the final speed (or near enough)?
2. Can you play it without hesitations and stuttering?
3. Are you playing the right notes at the right time with the correct fingers?
4. Does it feel easy and comfortable to play?
5. Can you play it by heart, or at least with the music in front of you without having to laboriously read it?
If you answered yes to 4 out of 5 of these questions it is mastered enough for you to consider this a good size and start working on it.
Do these questions apply to hands separate or hands together? Hands separate. Hands together is part of the work you will be doing once you decide the size. Unless of course you can do hands together straight away, then don’t bother with hands separate.
If you can master ten bars after seven repeats this is the size of chunk. It is neither too large nor too small. I have mastered 200 bar pieces (the whole piece) after seven repeats and went on to perfect the piece in the next ten minutes. It was an easy piece (for me). I have also struggled with half a bar for over a week before it “clicked”.
Surely you have experienced this “click”, this very magical moment when your fingers just seem to know what to do and everything flows effortlessly. This is what I mean by “mastered”. Of course, this is when you are ready to
start learning the piece, so do not let this word “mastery” confuse you. Ultimately nothing is ever mastered and you can always improve. But there is this moment when you finally “get it”, which is of course the instant when practice really starts. Whatever you did before this moment was investigation and terrain recognition. (Which of course is very important)
There was another piece instead where I could just master 1 bars after seven repeats
Now, I'm doing 20 minutes sessions for each bar
Since the piece is 140 bars long, does that mean that I have to spend 140 session (140 days, since I have more than one piece to practice daily) to master the whole piece? (there are no repeated patterns or parts, every bar is different)
Analyse this piece. Are all of the 140 bars of the same level of difficulty? I doubt it. In fact a large amount of these 140 bars will probably be repeats, either exact repeats, or repeated patterns, so that what you learn in this one bar will very likely be easily transferred to other, similar bars in the piece. It is very important to spend time identifying patterns, so that you put a lot of time and effort on a pattern , and then wheeze through any similar patterns you may find later.
But to answer your question, yes, if you have to work on a bar at a time, then that is what you have to do. What is the alternative? If you cannot cope with one bar, surely you will not be able to cope with 20.
I've noticed that Bernhard when explaing how to practice a specific piece usually start from bar 1 to last bar
Are there exceptions where you'd better practice only the hard bars and let alone the easier ones?
Could that be the case?
Starting on the first bar and going all the way to the end is actually the exception. 99% of the pieces you must identify the most difficult bars and start with those. The most difficult bars in a piece will contain all the technique necessary to play the piece. So by working on the most difficult bars first (which are usually just a few) you will be saving a lot of time, since once you master them, the other bars will come easily.
If a piece consists of similar difficulty bars with no especially difficult bars, then it is a really good idea to start with the last bar, then add the penultimate bar and so on. This is a really powerful learning trick. If you start on bar 1, then bar 2, then bar 3 and so on, you are moving from what you know to what you don’t know. But if you start at bar 100, then add bar 99, then bar 98, you are now moving from what you do not know to something you already know. Logically, it should make no difference, but psychologically the difference is staggering. Try it!
So, no, usually you do not start at the first bar and proceed in order. Usually you start with the most difficult bars first (I call this “preliminaries”) and once these difficult bars are mastered, you proceed to learn the piece back to front.
The problem is that when my teacher at school says that I have to "master" bar 1 to 125 HT of a piece for the next lesson, I have to do it within a week so I can't manage 20 minute sessions that doesn't allow me to complete the piece in a week
So, maybe I should practice less than 20 minutes per session
I said this many times before. 20 minutes is not written in stone. If you can master a bar in 2 minutes, move on! Why keep practising what you have mastered? On the other hand if after 4 hours you have not still come to terms with a passage something is wrong (usually you are tackling a too big chunk). And then you have the obsessives who master the passage after ten minutes, but cannot stop themselves and keep at it for the next 6 hours.
On the other hand your teacher’s expectations maybe unrealistic. As a teacher, I would rather my students brought back 20 bars perfectly learned then 125 in a mess. But then this is just me. Each person has its own optimum learning rate. Some learn faster, some learn slower. But it is the end product that matters.
Alternatively you may need to make a plan: How are you going to break down these 125 bars so that they do get covered in a week?
I think you are overcomplicating matters. This is simple stuff. Really.

Best wishes,
Bernhard.