That's cool. I guessed wrong about your level of ability.
I often get asked to pick a tune, then play the melody and solo, on combo gigs. It adds variety, and audiences seem to enjoy it. My "formula" is to choose a ballad (not too slow, or it drags) or medium swing, and play the melody by myself before letting the band in to accompany my solo. I always count the band in, because invariably somebody isn't paying attention and misses their entrance. Sometimes I choose:
Easy Living
Lover Man
When Sonny Gets Blue
In A Sentimental Mood
If you're up to it, I suggest upright, arco.

There's a good chance that nobody else will play a ballad, and they really do sound nice on bass. The girls will melt.