Look into Blackstar pedal. They got them from clean preamp to overdrive to distortion to more distortion.
Amazing pedals.
I have no experience with my guitar through Line 6 POD... but I've run my bass through guitaramp models on a POD X3 into my bass rig.
Pleasant results and to the extremes my bass sounds like it's been played through a guitar rig.
Edit: also a plain guitar distortion pedal that might suck on bass (subjective) through your bass rig might sound wonderful with a guitar.
In the long run you might be getting a guitaramp though.
Fender has a nice small amp, the Champion 600 wich is small and cheap... for bedroom practice only off course.
