I'm not a Bass guy, but from a guitar perspective it sounds doable. Treat each pickup as its own circuit, use a stereo jack, and plug into something that'll take the stereo signal. It sounds like it might get a little cramped in the cavity with two preamps and possibly two batteries (separate or shared 9v-18v depending on power needs), but I'll have to defer to our local bass builders on that.
Normally the stereo portion of the jack is used as a master on/off for the onboard electronics. If you don't figure in an extra switch or push/pull for this it'll probably eat batteries. Just my 2 coppers