the main difference between a keyboard and a bass is the dynamic envelope of the sound IMO. Adjusting your playing technique, and some clever use of a compressor should be able to get most of the way there. If you had the attack on a compressor set pretty slow, you could kill off the sustain of your notes. Roll off the tone, play very, very cleanly, maybe with a pick, being very consistent with your picking velocity. Then you could add some modulation and dirt etc after to shape the sound of the "keyboard".
I've not actually tried this but will give it a go ASAP. In the past I've always gone for more synthy sounds, so octave down, play higher up, put a load of dirt on, sounds a bit synthy, but definitely not like real keys