Sounds like a pretty pretty weird to me too! Altho not quite as weird as a couple of years ago when I had to walk a chorus of 'I only have eyes for you' with a free tuba and bass sax solo going on!
Best chance you have of making it work is to play as far away from the register the other bass player is playing in. When he plays low, you play high, and vice versa.
Alternatively you could play a bass line a tone away from what the other bass player plays at all times just to make a point!
If you're talking about how to construct a line, that's a different matter, loads on TB about building walking lines - the theory behind that is transferable to any style. To summarise, play chord tones on beat one (and often beat three as well) and find nice melodic ways to link them using scale notes or chormatic passing notes.