I think
garfy has covered things pretty well! Just some extra thoughts/notes ....
The Rick bass is probably a big part of the sound. Most stock 4001 and 4003 models should be
similar to what Paul used (technically, a left-handed 4001S), though Paul's bass would have had a real "horseshoe" Rick pickup of the sort that was phased out of stock Ricks in the (I think) early/mid-'70s, though you can get replica models of those. And, then, Flatwound strings, I should think, and played with a pick.
There is conflicting info on the kinds of signal paths used, though given the opportunity for effectively unlimited studio experimentation the Beatles enjoyed during the recording of Pepper, one doubts that one size necessarily fit all.
The late, lamented Geoff Emerick has claimed that he always mic'd the bass -- and perhaps DI only came in when Ken Scott was engineering the "White Album" sessions, though nevertheless it at least would not
surprise if some of the bass tones on
Pepper were DI or a combo of mic'd amp and DI. As
garfy notes, bass amps were probably Voxes, and perhaps even more probably the somewhat obscure UL730 and/or UL 430. The 730 was intended for guitar and the 430 for bass, but they were basically identical except for, I think, a tremolo circuit on the 730; I think McCartney is on record as having used both on different given songs on
Pepper. These were hybrid amps, with a tube power amp (similar to the power amp of the AC-30s) but a solid-state pre-amp. Since AT's "based on Vox" amp models are mostly AT2-vintage, you might be able to play around with "based on AC-30" models but swapping in a solid-state pre-amp model of some kind. The speaker cabinets were 2x12 with Celestions, I think, but I don't know more than that. (Perhaps similar to whatever AC-30s of the period had, though!) It's understood Emerick liked to put the bass cab in the center of the room with a AKG C12 (with a figure-of-eight pattern) several feet away; so, as
garfy suggests, try a big studio room with a Condenser 12 mic model backed off some distance (and move it around until it sounds good!). Photos show STC 4038 ribbon mics as well, though I don't think AT has a model for that; I've also heard Emerick would use a U47, though I don't know if that's true. I understand photos also show a Fender Bassman hanging around in the Pepper sessions, but I don't know whether any bass was recorded with it.
Also, my feeling is that, whether mic'd or direct, the bass signal probably got a
healthy dose of Fairchild compressor -- since Emerick slathered that all over everything
-- which is specifically modeled in T-Racks, though I kind of feel like the Tube Compressor from the AT Hendrix package can serve as a "within Amplitube" stand-in. I would start with a slowish attack (around 38ms?) and perhaps the fastest release possible (50ms?). Dial in the input gain to get a few dB of reduction (or whatever the little green lights on the model might indicate), or whatever sounds good, and adjust the output appropriately.
Then, I suppose, for yet more nerdy authenticity questing -- besides cloning Sir Paul's fingers, etc. -- one would want a chain in the DAW with the appropriate models of console and tape machine.
I believe some companies may make such emulations, though not IKM.