How you approach Bach is really dependent on your personality, technique, experience, and how far into the piece you want to go.
His music really has endless possibilities for nuance, interpretation, and understanding At one side, you could just learn the notes and go by intuition for phrasing, on the other side, deeply analyze the piece, and map out your articulations, phrasing, dynamics, you could even use the music as solfege exercises, or transpose the piece to all keys. Many musicians in his day were versed in figured bass and composition, the divide between performers and composers was not very wide, so his music would have been used to teach models of composition and harmony, even improvisation.
I like to use a tanpura drone for intonation, and a metronome to get the rhythm precise. You don't want to perform too mechanically , but when learning it is helpful to be disciplined. Breaking the piece into smaller segments is helpful. Before you begin ingraining the piece, make sure you have the fingerings and bowing in the part, and depending on your level you could have the articulations, phrasing and dynamics mapped out too. But, I have found that having too much detail at the beginning is stifling and makes the work even more tedious. First start with 2 bars, practice until it is in the muscle memory (I usually do 10 repetitions, and only count the perfect reps.), then 10 reps of 4 bars, 8 bars, 1/2 & the complete piece. So by the end you will have played the piece 50x total, with good technique, because that is what you want to ingrained in your muscle memory. But remember that practicing is like exercising, you can't expect to be able to nail something the first day, it is a process that builds over time. Then record yourself performing the piece and critique your playing, and do the same rep. process incorporating your critiques. So by the end you will have played the piece 100x, and it will be ingrained. But this process is only for music that is important to you, because it is so time consuming. But I think that Bach is worth this kind of work.
After a while you soak up all you can from a piece and it is time to move on to something else, the more you go through Bach like this, the more sophisticated your interpretations and process will become. When you come back full circle to the original piece your playing will be in a different place, technically and musically, but initially you have to do the busy work.
I think you can perform Bach, really any way you want to, but it is important to always ask why you are making a certain decision, from a musical or technical standpoint. Why this fingering or bowing, why vibrato or no vibrato, etc.
And if you are informed and have done the research to form your musical opinions, than who can say your approach is wrong?