On a passive, bolt-on fretted bass (I've never own a neck-through or a set-neck):
19% - Pickup Location
17% - Strings
16% - Pickup Type: Single Coil, Humbuckers, etc.
13% - Electronics (Pots & Caps) Electrical Values: 500k pots, .047uf caps, etc
12% - Electronics (Pots & Caps) Quality: difference between quality components and very cheap components
11% - Pickup Model: Difference of swapping a single coil, for example, with another single coil in the same pickup location
5% - Bridge
4% - Fretboard Wood / Finish
3% - Body Wood / Finish
On a passive, bolt-on fretless bass:
18% - Pickup Location
17% - Strings
16% - Fretboard Wood / Finish
12% - Pickup Type: Single Coil, Humbuckers, etc.
11% - Electronics (Pots & Caps) Electrical Values: 500k pots, .047uf caps, etc
10% - Electronics (Pots & Caps) Quality: difference between quality components and very cheap components
9% - Pickup Model: Difference of swapping a single coil, for example, with another single coil in the same pickup location
4% - Bridge
3% - Body Wood / Finish
This is all based on my experience with the few mods I've done and basses I've owned. YMMV of course.
I didn't include technique, because I related this to the same person picking up a few basses in a store and using the same technique on all of them. We all, or should, all know the different tones we can get when we play this way, or that way.