If everything else is super busy, it might not be a bad idea to lay back. However, it sounds like you know generally what's going on, and no doubt you've considered that option, so let's look at what we can do to jazz things up a bit. My first thought is that you should complement his lines by filling in the gaps: if he's playing something syncopated, compose figures that keep the beat, and if he's playing something really downbeaty, then get the syncopations. Those little spaces in the music are where your musical slime mold can propagate. If it worked for Stravinsky, it can work for you.
Next, there's this harmonic thing. Note choice can be tough. You can always do chord tones and try to navigate through the changes with the best voice leading you can manage. If you've never studied counterpoint, it's a fantastic way to get ideas on how to compose lines with good contour. You probably won't study counterpoint for this band, though, so let's go a little simpler. I'd say that the most important aspect of any line is its rhythm. Rather than bogging yourself down thinking what notes you're going to play, you might find it easier to make a concept for the rhythm. Listen to what your guitarist is doing, then try to imagine a very vague bassline. Try it with a fast rhythm, a slow rhythm, and then a medium rhythm, and also ask yourself if you should be syncopating (if the guitarist is playing a lot of downbeats) or if you should be holding down the rhythm (if the guitarist is syncopating a lot). After you get some good rhythmic guidelines, you might even be able to get away with jamming one note the entire time, although you'll probably want to develop that line so you're playing cool notes at some point.
A good example of interlocking rhythms used between two voices in a composition (J.S. Bach's Two-Part Inventions, No.6):
https://www.youtube.com/watch?v=sLJi3G4QPaU
Another option, if he's doing a lot of arpeggiation, is to find a voice in his chords that you can follow. For example, if he has chords that have a low note and then a few high notes, you could probably double up on the low note, which would effectively make you an extension of the guitar and also have the added bonus of a greater sense of harmonic support (since you both would be hitting that note). Something along those lines goes on in this tune (Mahavishnu Orchestra - The Dance of Maya):
https://www.youtube.com/watch?v=Q1qIQjUy5B0
