A lot of useful info has already been said. Before even getting into the ampless aspect of it...
1 - Bi-amping was a thing in the 80s that's technologically obsolete now. It was done to get around limitations of the gear at that time, and never worked
that-that great to begin with. The super-abridged version is, most bass guitar gear wasn't great at amplifying the full range of signal basses create. Low freqs require more power to reproduce than mids or highs, as well as having different acoustic properties and needing different material characteristics for the speakers and cab dimensions, etc. The idea was to split the signal into two bits, and let gear that's good at reproducing lows reproduce lows, and gear that's good at reproducing the rest of the freqs reproduce the rest. In theory. In practice it probably introduced as many issues as it solved.
But, if your amp and cab are less than 25 years old, it's probably technologically sophisticated enough to do on its own what bi-amping was trying to achieve. Modern amps and speakers and cabs are more efficient, louder, and more-full range. Gear that has less-than-full-range frequency response curves, or "baked in tonal voicing" are now designed to be that way to cater to peoples preferences, not because it's the best the technology can achieve.
2 - Even if you were using gear from the 80s that required bi-amping, if you're not amping your bass, you can't really bi-amp it.
On top of that, you're sending your signal to the PA, and the PA is sending it to the PA Mains. The PA mains have crossovers that split the signal and send the lows to the Subs, the Low-mids & High-mids to the woofers, and the highs to the tweaters. The PA is essentially doing what you're trying to do, breaking the signal up into frequency ranges and handling them by different power amps and speaker styles, and it's probably doing it better than a bi-amped bass rig ever would.
3 - Splitting signal can still be useful for other things. If you want to have one clean channel and one with FX on it, splitting can be nicer than just using a dry/wet blend. You have the full-range clean signal, and then on the FX channel, you can use a HPF or cut a low-shelf to pull out a lot of the low frequencies before any FX because a lot of FX don't play nice with bass frequencies.
I have a project where i need to split my signal into 2 channels:
Bass --> tuner --> HPF at 20Hz just to remove subharmonics before the compressor --> compressor --> ABY Mix splitter --> ...
--> Chan 1 - "Bass channel": Preamp --> Audio interface --> Ableton Channel 1
--> Chan 2 - "Sub channel": 1 octave down 100% wet --> LPF at 220Hz --> Audio Interface --> Ableton Channel 2
That gives me a bass chan and sub chan, and those two channels are then sub-grouped again. It allows me to put different FX on the bass channel, or sub channel, mute each one individually, and then put FX on the subgroup to treat them as a unit again.
I'm doing this for House music and Drum & Bass/Jungle. You might not want the Bass & Sub-bass split. But a similar setup would work just for Clean & Distortion/FX split. That might also be overkill for a church band, and your sound engineer might give you side-eye and be annoyed they have to now set up and mix 2 bass channels. Blending multiple bass signals is a major p.i.t.a., and if you don't have your FX channel already set up to blend perfectly with your clean channel, again, you could cause more problems than you're solving. You could just get fx pedals with dry/wet blends not overcomplicate the situation.