When you pluck a string, some of the string's energy is retained in the string, some is transmitted to the body and some is dissipated. If you could find a way to retain 100% of the energy in the string, then you would only have the sound of the electronics and the strings, and the wood wouldn't make a noticeable difference.
Earlier in this thread gweimer mentioned the 2Tek bridge. It's so massive that it keeps most of the energy from being transmitted to the body. That's why you hear people say that it makes most basses sound similar, or I've heard it said that it makes almost any bass sound like a 2Tek. Well, it doesn't make a bass sound like a bridge, but it does keep a lot more energy in the strings.
That's also what happens when you put a massive bridge on a Fender. Not as severe as a 2Tek but still, the inertia keeps more of the string energy from the body. Some people like this, some don't because it sounds less like a traditional Fender.
BP did an Alembic tour years ago, Micah Wickersham explained that reason for the heavy brass bridge attached to a brass plate sunk into the body was to neutralize the tone of the wood as much as possible so an Alembic would sound like an Alembic regardless of top wood. And they chose mahogany for the core wood because they felt it was fairly even across the spectrum.