I've attached a small, fairly basic pdf I put together a few years ago with some useful chord voicings for 4-string bass. In general, these sound muddy below the 8th fret. Of the chord tones (1, 3, 5, 7), the 5th is by far the least important. In a Dominant chord, the 3rd and b7th are the most important, although root motion is also important. This chart will get you into some ideas for standards like All the Things You Are, etc. So, basic voicings. But once you get familiar with these, constructing voicings for more complex chords will become easy.
Sometimes you are faced with a decision. For example, if a Dom7(#9) chord is called for you probably don't want to voice both the 3rd and the #9 (even up the octave, the #9 will usually sound awful in a bass voicing if you are also voicing the 3rd). So, depending on context, you sometimes have to accept some limitations associated with bass.
As far as comping and voicing go, one of the things that's often characteristic of jazz is the ability to change just one note in a voicing to move from one chord to another. This is really mainly an artifact of rapid tempos and the need to shift as little as possible at tempo, but the result is a characteristic style (at least on guitar as we are now translating to bass).
For example, here are two additional voicings not in the pdf I attached (I don't count the D voicing because it's an open voicing; all the voicings in the pdf and the first two below can be moved around and rely on no open strings). The chord progression is: | Emin7 \ \ \ | A7 \ \ \ | D \ \ \ |
Emin7..A7....D
G 12....12....11
D 12....11....O
A x......x......12
E 12....12....x
Have fun.