Group playing around a single mic is a difficult skill. It's a complex dance between all the performers. I once saw a guest mandolin player get hip-checked and land on his ass when he didn't get out of the way fast enough. The audience loved it! Hardly any bluegrass bands actually use only a single mic. Even the minimally mic'd ones use at least two or three or four main mics and a dedicated mic on the bass. Typically one or two vocal (& fiddle) mics, often a large diaphragm mic, which looks cool, up at head level and a couple shared instrument mics on either side down closer to waist height guitar level.
The Chat.Co.Line setup is somewhat of an halfway compromise between those things with all three main mics mounted on a single stand, which should make for an easier guerrilla location setup. It still takes some dancing, though not as much as trying to use a single mic for both vocals and instruments. The guitar needs to get in close, the banjo can hang back further than anyone else, 'cept the close-mic'd bass.
Might be worth a try to use a 4 ch recorder with decent built in directional mics, with the recorder attached to the same stand below the large diaphragm vocal mic. That would be similar to the Ch.Co.Line setup. Run the bass mic into the other XLR channel opposite the vocal mic. That's sort of the stage lip + vocal mic + bass mic thing.
..It is out of your price range but DPA offers a really nice clip on instrument mic for upright bass. IMO that is the best approach to that instrument. A lot of professionals use this and if they can get a DI for the bass in larger settings will ask that be used.
That's the DPA 4099 (B for bass version I think) which is excellent for that and pretty standard these days. The 4099 is a go to mic for live "clamp on to the instrument" acoustic instrument mic'ing. Same mic is used on fiddles, mandos, banjos, horns, etc. The only difference is the clamp specific to each instrument type, although the horn version may be less sensitive.
You'll want some kind of mic mounted on the bass itself like that. You may be able to get away with the classic technique of simply wrapping a regular mic in a towel or bit of foam and stuffing it behind the tailpiece pointing up at the bridge.