Enough to know what you are hearing; at least for yourself, if not to be able to tell others what you want.
At a minimum to be able to hear the root of a chord, know the quality of the chord [Maj, min, Dom,Aug, dim].
Knowing intervals so as to hear root movement in chord progressions. Also to figure out riffs and signature licks.
Learning the more common chord progressions.
It's good to know/learn/hear inversions - root, first, second - so you can spice up your lines a little instead of always nailing down roots. They're pretty easy to learn and you'd recognize the sound - esp if you play reggae.
Beyond that I found it useful to know how to build chords off of chord charts. Here again where knowing inversions and chord tones is helpful for quickly thinking smooth basslines through chord progressions, instead of always jumping from root to root.
it's good to learn and hear the signature sound of the different modes and get them into your fingers for runs (kind of in auto mode if you are singing when you are playing) - this also helps for hearing your way through weird alternate chords and subs if you are doing jazzy/fusion stuff.
Also fun to think about counterpoint, so you can build fun counter basslines over guitar runs and licks, unless you are totally happy following guitar lines.
This is the stuff that helped me most onstage thinking up ideas, and jamming on the fly, quickly learning songs, and hearing in my head so I could write songs on bass and tell others what I wanted to hear or correct them if something was off = "that's a minor, not Major","I'm playing the third there, that's not the root","It's a second inversion, so I'm pedaling the fifth".


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