I've done chromatic permutations exercises for ages on the guitar. They are the most misunderstood technical exercises ever.
First, I disagree they are strength exercises, simply because there are NO strength exercises at all. Your hands and fingers already have more strength they'll ever need for playing. Maybe the exception could be some bending but that's it.
Quite the opposite in fact these exercises should lead you towards decreasing the strength needed and relaxing you more.
However, the large size of low frets on a bass makes them a lot more challenging than on a guitar, so for most people it's really hard to relax in the 1234 range because we need to stretch the fingers which definitely adds a lot of tension, defeating the purpose.
Actually, the real purpose of chromatic permutations is finger independence. Playing relaxed is more like a requirement, but because we all tend to tense, you can say that relaxing is the first purpose here, which enables practicing for the second purpose of finger independence.
With guitar, the amount of students who really don't get this is staggering. Many spend hours a week with 1234 chromatics and NEVER move on to the actual permutations which are the real deal. That's because they waste all their practice time thinking they have to cover the whole neck length every single day, and they repeat the whole drill at different increasing metronome speeds, then after an hour of self-imposed torture they of course have enough and move on. But they never relax once during the whole thing.
Taking into account the bass differences, my suggestions to you are:
- keep the purpose in mind: fingers independence while relaxing more and more
- use all 4 fingers, one per fret, no shifts
- choose a range when you don't need to stretch or stretch is minimal (e.g. 5678-9876)
- you can move up and down the neck a bit but you don't need to cover it all
- don't use the metronome (this is NOT a timing exercise and the metronome will tense you up), practice free time so you can instantly slow down when you notice your coordination is not great and speed up again without interruptions once your fingers get the pattern
- by all means practice at least SOME permutations! In fact the basic one 'index-middle-ring-pinky' is the least important
Now, improving left hand fingers stretching is another matter altogether. You CAN also use these exercises for that if you want, though there are better ones. In that case the permutations cease to be important, you can stick to the basic one. If you want to focus on stretching, move down the neck gradually from your comfortable range rather than starting in the 1234 position, so that you don't stretch too much at once. Spend a little time there but then go back to a less stretching range. Back and forth between more and less stretch a few times. Don't shift, use one finger per fret. Shifting allows you to PLAY more comfortably by avoiding stretching, but if you are practicing to improve stretching well you got to stretch!
There is another weird possible misconception behind the corner: that you are allowed to do anything that works for you to do what is written on the exercise, but that is true when you PLAY music, not when you practice a technical drill. You need to seek the purpose of the drill, not fulfill what's written on the tab.