Hi Guys,
Dont know if this has been covered as I haven't read all the comments but the wood of the bass is a major factor IMO. I'm starting a guitar workshop myself so have done a lot of research into these matters. What I have gathered is that wood, construction and pick-ups/EQ have the main inflence on a basses sound. It's the middle section of the guitar that makes the sound, the edges (horns etc) dont.
Generally speaking softer woods, like mohogany create a softer, deeper tone. Harder woods, maple for example are brighter and have more attack. Ofcourse you can mix the woods to get a bespoke sound.
A good combo of wood is mohog body, maple top, maple neck, rosewood fingerboard. you get body and warmth from the mohogany, attack from the maple. maple is strong for the neck and the rosewood is strong and dureable for the fingerboard. it's also not too bright. Then you gotta pick construction. Bolt is brighter, glue-in is similar but not as bright. then pick-ups etc etc.
Hope this can help.