Some people are very adamant about using a mic over a pickup. For recording where you will have isolation from other instruments and monitor on headphones, I would opt for a mic. A mic will tend to sound significantly more natural than a pickup, although some modern pickups sound very good.
The problem is upright bass is not really loud enough acoustically. The mic will pickup whatever sound is present at the capsule, and if other instruments are louder than the bass, then they will dominate in the mic signal.
The volume differential also relates to the sound of you bass coming back from your amp. As you turn up the amp a feedback loop forms. At low amp volume, the feedback loop changes the frequency response and decay characteristics. The feedback loop causes the bass to sound progressively unnatural as you turn up, and greatly limits the max volume. As you turn up, at some point the amp will break over into feedback. In my experience using a mic with an amp will not allow you to get louder, but it may allow you to fill out the sound a bit. How loud you play acoustically is a significant factor.
If you have to use a mic, consider how you can isolate the mic from the sounding coming from your amp and other sound sources. Mic aiming helps some because most mics are directional. But some frequencies will tend to reflect back off the curved surface of the bass. The curved surface causes the sound to enter the mic at slightly different times, which creates flanging. The flanging on cymbals is particularly bad. It really helps if the drummer is playing with a light touch, which is not possible in a big band setting.
You can also consider the distance of other sound sources and the angle in which sound will arrive at the bass and mic. In studio settings it's common to use sound shields called gobos, which block and absorb some of sound so there is better isolation at the mic.
If you are placing the mic on a stand, rather than mounting it to the bass, something like this may help block some of the highs and mids:
I am not necessarily telling you to buy a gobo or mic shield. I am primarily training to explain the problem, which tends to be rather severe. IMHO, Use positioning and whatever resources you have, and then accept the limitations until you can get a pickup.
Good luck!