To play bass well, you will need to know how to shift positions confidently and move up and down the neck based on what you hear. A good exercise is to learn to play melodies and scales on a single string. Try Twinkle twinkle little star using just your index finger. Then On top of old smokey. The intent is to make you shift your hand comfortably. When you do this, note the interval that you are shifting to relative to the chord. For scales, use 3 or 4 fingers as you refer. I play scale modes in order, major, mixolydian, dorian, aeolian, etc. Note which notes shift as you change mode. Happy plucking
Yes, one of the hardest things I had to master right at first was is the next melody note a jump of one fret or three. Is it up scale or down scale was not as simple as it sounds. That took some real time until my hands and ears were working together. Get that on one string, then tackle all four. Happy trails.
One of my favorite exercise is to play triad arpeggios on one string. Pretty hard at first especially to play it clean without slurs...
With my enhanced ability to break strings, it was my reality while playing live - I didn’t need any special exercises.