I'm gonna suggest something that seems contradictory to what's normally done. I've successfully recorded many of the most famous jazz bass players in history, both live on stage and in the studio, and this has worked well for me.
I suggest trying a small diaphragm condenser mic like a Neumann KM83, suspended with rubber bands in the bridge. (Don't use foam as this chokes the bridge and the bass won't sing.)
Yes, this is a OMNI mic, NOT a cardoid. I'm not a big fan of cardoid mics (or figure 8) mics on bass because they always exaggerate the low end due to proximity effect. I find that I have to roll off this boost to get a natural bass sound. A good bass player with a good sound won't need any additional bass boost, from proximity effect or EQ.
Omni mics don't have proximity effect. The sound more natural when micing everything close. The KN83 has a very smooth off axis response, pretty even across the whole frequency spectrum, with a bit of attenuation, making any leakage sound less colored than the typical off axis response of a cardoid.
Also, having the mic so close to the body and strings let's you take advantage of the 3:1 rule. Leakage energy will be 1/9th as strong as the primary source.
In most jass recordings, there will almost always have leakage because there are usually no overdubs for the bass and everyone prefers to be physically close for better communication. This leakage can be your friend IF it's lower in level AND sounds natural.
I suggest giving this a try. Be sure to have everyone closer rather than spread far apart. And try to have the bass player position his back and the back of the bass to the most offending leakage source.