Best thing to put into the sidechain to start off with is an eq pedal. specifically one that can do HPF , or maybe a parametric eq ... very helpful. A multiband graphic eq is less ideal but can still work.
As a bassist, that will let you control how much the low E (and B) string loud fundamental notes trigger compression versus playing up the neck.
Although it's possible your bass compressor pedal already has a HPF in it's sidechain (the stock sidechain, not the optional external one we're talking about here).
FYI every compressor has a sidechain - it is just normally not exposed to us. It is the trigger circuit that is required for any compressor circuit to actually trigger the compression.
So, if you get a lot of compression on low notes but not nearly as much up high, you can put a HPF (high pass filter) in the sidechain, filtering out the low notes, or at least lowering their level. That way the lower notes won't send as strong a signal back into the compressor's sidechain input, and therefore won't compress as much. Meanwhile if the frequency of the HPF in your sidechain is set to the appropriate frequency/filter/slope etc (depends on eq you use and your preferences in playing and experimenting with it), you can get it to give you a ton of compression/sustain up high when soloing, or even for popping in slap/pop while the slapping comes through more loudly (slap is often lower strings, popping is often higher strings, for example).
For crazy effects sure you can use a sequencer or other fun stuff.
What I'd try is some kind of a random filter - that could be fun.
In dance music (in the box, not typically wiht a real drummer/bassist combination), they often put the kick drum into the sidechain on the bass, and often on nearly all of the music.
That gives that famous oomph oomph oomph sound where the kick drum is super clear but every time it plays the rest of the music goes silent (or very quiet) for a fraction of a second. If you time the compressor release just right, you can have the compressor bring the music in a half beat after each kick drum (or whtaever you like) and it gives that huge dance beat thing people love at clubs.
Just so you know what a sidechain effect sounds like.. at it's extreme.
FYI - I build compressors - I built an 1176, and am currently building an opto compressor based on a pedal and doing a lots of circuit mods to it to make it as close to a cheapo LA3A sort of sound. Yes I build them from circuits already in existence and even from pre-bought boards. But I do learn the circuits and adjust them where possible to do my bidding. It's super fun when it works, and you learn a lot when it doesn't.
A lot of my mods on both compressors are related to the sidechain, mostly based on filtering by frequency.
