It started off as me trying to find a sound something between Tony Levin (circa Thrak-era King Crimson) and Justin Chancellor, which gradually morphed into its own thing to accommodate my tastes and playing technique.
I used to be a fairly heavy-handed player, but I'm playing with a far lighter touch these days but I still want things to sound big, so I'm using two compressors in series, Levin-style, to control the dynamics, then, in terms of EQ, notching out that boxy-sounding 800Hz frequency range and gently boosting low and high mids. I also mostly play a 6-string these days, so I've had to adjust the EQ and compression to accommodate the high C so it doesn't sound brittle compared to the others. I also have an alternate version of this sound for fretless where I don't dial out the 800Hz range, since that's where a lot of the "mwah" lives in the frequency spectrum.
I'm currently using a Headrush Flex Prime for effects - not a popular choice for bass (it doesn't have many bass-specific effects, amps or IRs), but it's small, powerful, easy to use and does everything I need it to do. It also came with the ReValver amp modelling software, which I used to model my previous Zoom B3n-based tone, directly from the pedal, so I had a good starting point to go from there.