Geez, so many different processes here. Everyone is doing something a bit different for something we all do. Gotsta have bass, but we're all doing it a bit differently. That's pretty cool.
To throw it out there, the DI/virtual Ampeg Pro(no cab)/TSE channel is working very nicely in my current project.
I'm still using my Digitech pedal board, the old GNX3000, for all my guitar and bass tones. I actually have two of them, one for live and one for recording. It has about 10 different bass heads and cabinets, I also have a bunch of amp/bass amp sims plugins, but whenever I A/B I just like the board better. I move around a bit on the board with the bass heads/cabs I use, but for the last 10 recordings or so I've stuck with the Fender Dual Showman through an Ash 4x10, which the manual says it's an '03 Ash ABM 410T, I just like how that pairing sounds. (For guitar tones I'm obviously all over the place)
I've been wanting to experiment with a DI box and print two tracks, one clean and one through the board, but haven't done it yet. I'm mainly using an '06 USA P-Bass, and I usually just high-pass around 70-80, and usually remove some rumble in the 150-400 range, just a few db's, depending on the mix. Then into the Slate VTM, Slate VCC, Slate FG-Stress or Waves CLA-2A (sometimes after a CLA-76 if the transients are too poppy) then the Waves MV2. I'll usually parallel compress the bass as well, depending on the song. Occasionally I'll send it some SansAmp or Avid Lo-Fi, again depending on the mix. I've been hearing good things about the Slate FG-73 on bass too, have it but haven't tried it on bass yet.
All this talk on cabs bringing in mud, makes want to try turning off the cabinet and just trying the Ash head by itself (board gives that option) and maybe I won't get that rumble I was talking about. Hmm, yea I'm trying it on the next recording