In the time that I've been here, I've noticed that, (and I'll be vague, since everyone's specifics are ever changing, depending on who you ask...) type of wood is a really big factor in the quality and sound of a bass. Density seems to be able to change or determine tone of a bass, somewhat, and in doing so, even determine what sound the pickups will be trying to reproduce.
This is true, also for the neck, since it is essential that it's a stable wood and able to withstand the stress of the string tension.
Then there's the hardware that has to be reliable enough to hold, and adjust the strings to the proper tension and distances without any variation after being properly set.
Then there's the pickups, that will be the sole enterpretive factor between the sound of the wood and the sound that's sent to your amp; (That's a whole 'nother book...)
THEN, if you have active electronics, there's the eq factor and looking for the best of the best to boost the sound your pickups are sending out.
After that comes the amp, and the playing ability of the bassist/bassplayer,

which can make or break a good bass, sometimes

, but that's not the question.
That's my take on it IMHO.
