I am an upright bass player of nearly 20 years, and I record myself all the time.
It all depends on whether you have isolation or not. If you are recording jazz, you probably don't. In general, the sweet spot will probably be around the soundpost, which is around the g-side bridge foot. Do not mic in front of the f-hole. Another good spot is right at the tip of the bridge pointing at the bass. Upper bout like Agcurry said is good if you have iso.
If there is no drummer in the room, you should be fine with a couple of gobos. If there is, you need to make a decision to fight the bleed or embrace it. For fighting it, I would use an RE20 or similar placed as close as possible without getting wierd resonances. An M88 is good too, but I really prefer mics without excessive proximity effect. Rolling off too much bass with EQ will hurt the overall sound. If the player sits, it's easier to get the mics closer. Gobo the hell out of the bass.
To embrace the bleed, I put an earthworks omni (or another light-weight condenser with good off-axis response) suspended between the bridge feet with rubber bands. I use an omni so I can get it right up to the bass with no proximity effect, maximizing the bass sound and minimizing the bleed. What does bleed should be usable. Make sure the players are arranged the same way they get panned.
If you have the free tracks, I would do it both ways. I'd even take a direct signal. The DI will likely not sound good, but you might get lucky depending on the pickup he has.
PM me if you want to hear a sample or two. Also, why don't you list all of the mics you have available for the job so we can recommend one?
Don't know what your mixing tools are, but in mixdown I usually high pass around 65hz, and apply Voxengo Soniformer to smooth out any resonances that jump out (depending on the room it was recorded or how the mics had to be positioned to minimize bleed). Good luck.