Why not?

This is part of the basis behind bi-amping.

 

There were actually those who did that exact thing back in the day (I think Chris Squire used his 'Rico Sound' thing to run his bridge pickup through a guitar amp and bass pickup through a bass amp, for example).

Then, biamping came along in bass rig design, since back then, the components available didn't really allow manufacturers to produce true, full range cabs.

Today, IMO, there is little need for this. There are a variety of one way, two way, and three way cabs (with various combinations of woofers, mid drivers, and tweeters with nice internal passive crossovers) that will give you as full range of a tone as you could ever want.

It's a good time to play the bass guitar

 

+1 to Kjung, and yeah, Chris Squire biamped his Ric. His neck pickup went to a bass amp and his bridge went to a guitar amp.

 

I belive the one who do this isn't so much to get a full range sound, but for getting guitar like grit in the top end whilst preserving a clean low end. These days with amp simulators, and various pedals, you can simulate this with blend controls and judicious eq settings. But to do it well, you really need to bi-amp properly into separate cabs to allow highs and lows to breathe and stop fighting for space.

Billy Sheehan is another who does something like this, running 2 pickups into 2 amp, with switchable distortion on the top end, but he uses 2 bass amps as he likes the SVT tone for highs and lows. He does site Chris Squire and Ric-o-sound as another user of the stereo bass setup in numerous interviews and videos.

 

i wouldn't bi - amp in the pure sense of the word because bass and guitar cabs are not designed to be run in the narrow bandwidths that bi amping was designed for.

without going crazy and using seperate signals from each pickup i would suggest something i have done. you can use seperate speakers either hooked up to seperate amps or seperate sides of a power amp. The side that gets the guitar speakers should have some kind of eq to cut the bass a bit.

i do this sometimes by running into a preamp - one line goes right into one side of a poweramp and into a 15. the other side goes into a sans amp, cuts the lows, adds some distortion, and then goes into the other side of the poweramp and into a 12.

blending the signal of the sans amp straight in the fx loop of my preamp gets a similar sound, but not quite.

 

Look for a site that has Tom Petersson's (Cheap Trick) rig. He's been seen sending his twelve string through Hi-Watt stacks next to Rickenbacker Transonics next to Fender twins, all at once. I've emulated that set up (with a four string) by using a Hi-Watt/Ampeg/ Fender Deluxe rig and it pretty much filled the room. No note left behind. Not a great load in load out deal but worth the trouble occaisionally. I alomost neglected to add that I saw the SMV tour last year? and Stanley Clarke was definately using some kind of small fender amps for his stage rig.

 

I set up a GK 800RB (bi-amp) this way, though running full range so that both speakers get the same signal, but each reproduces it according to its design specs.
An Avatar 212 neo 500W 4 ohm handles the lows, while an EV 115 driver designed for bass, guitar (primarily) and PA, handles the highs through the 100W 8 ohm "Hi" output.
Works very well. Easily transported, light weight.