I had no idea what a DI was until a few days ago, but the bassist uses gut strings on his upright which apparently sounds bad through a DI but fine once routed through the amp. I have no frame of reference for this but I certainly take his word for it. I got a great deal on a Shure Beta 52a kick drum mic locally, so I think we might run that and a SM57 and take the better of the two or mix them. Should be interesting, but the main goal is to do justice to his sound.
DI is short for "direct injection" which is just a way of saying direct signal feed, colloquially referred to as a DI box when it is separate.
There are two places in the signal path where one might place the DI.
The first place is to split the raw signal from whatever pickup, or contact mic is coming from the instrument.
The "guitar cable" from the instrument is plugged into the DI box, and then that feeds the player's own stage amp rig, as well as the PA system.
The second place to take a direct feed would be to take the direct signal out of the instrument preamplifier, probably a duplicate of the signal which is sent to the power stage and speakers of the bass (or other instrument) amp.
Most modern pro bass amps, especially head units (just the preamp and amp, no speaker built into this part) will be equipped with an XLR and/or a 1/4" direct output jack, usually on the back of the box.
The local PA system will usually take whichever of the two is most applicable to their circumstance... (leaving the other for the stage recordist!?)
But this operation is contingent on a line signal of some sort.
Most electric basses have one or more magnetic coil type pickups, but these rely on the the physics of a metal string oscillating near the coil.
Now we learn that this particular bassist doesn't play with steel strings.
So much for pickups.
But in order to use an amp, there must be some sort of signal coming down the cable, and the amp must make something good from it.
There are ways to pick up sound from non-metallic strings, but they are acoustic in nature, rather than the electromagnetic pickup method of a single or double coil ("hum bucking") pickup.
If you have a free channel on which to record, it may be instructive to capture the dry signal from the DI.
Going by the real-world experience of the folks who know the gear, don't expect to rely on it for best audio quality...
I hope this info is helpful and not overly obvious or superfluous/off topic