I may come at this from a different perspective than some, simply because I've been playing bass on sessions for more than 35 years (have have owned Java Jive, a Nashville studio, for close to 20 years). But here's my take; anything with a reasonably clean, controllable signal will work just fine.
A large percentage (if not most) of the bassists who work at Java Jive bring custom racked Neve preamps (or Neve clones) as part of a rack that also includes a compressor - 1073's, 1084's or occasionally 1272's - line amps that have been converted to mic preamps. Others will bring DI's with line level outputs - Evil Twin DI's, Avalons, and even that Mic pre that Ampeg made for a while.
As it happens, I'm between rack setups right now - I'm generally using the Ampeg DI which (in my room) goes to a Great River Electronics NV preamp (a Neve clone) or (in other rooms) whatever the engineer wants to use.
Over the years, though, my session rack has included an Ashley preamp (more than 20 years ago), a Demeter pre (with the +4 mod, and which I regret selling), API, Daking, Great River, Manley, Vac Rac and a few others. Though I'm using a mic level Ampeg DI right now, I've gone through phases where I chose an Evil Twin (which I also regret selling), the Avalon, a REDDI, a Little Labs, Radial (both active and passive) and even the old standby Countryman.
Some engineers have me play through a REDDI, and one or two are happy with a Radial Passive DI - I'm fine with that, too. Since most standard DI's have a mic level output, a preamp is required to bring it up to line level. One studio I work in quite a bit uses a Daking preamp, another engineer prefers API, while another will use the console preamps. I honestly don't care; far more of the sound I want comes from my fingers and from the bass I choose to play than from the rest of the signal chain.
As I said earlier, I work in my own room quite a bit - and with something over 40 channels of outboard preamps at java Jive, I have a pretty wide choice when recording electric bass; I took a rack out for a project a couple of months ago consisting of a Manley Pre, Manley Enhanced Pultec EQ and a Manley Mono Vari-Mu compressor. Fun (and the client loved it) but when I got home, I put everything back in the studio racks, and took just a DI to the next session.
Since Mr. Fortino mentioned it, I'll add that I carried a Sansamp bass driver for a few years, and tried it a dozen or so times. Only used it on a track once. It's not clean or transparent, and while it was great on that one track, it never sounded good to either me or the production teamp. It may still be in a closet somewhere around here.
Now that I've blathered for far too long - I'm waiting for a turkey to come out of the oven - my point was that there is no magic bullet (unless it's a well restored 1073); once you're above the entry level of Behringer, Alesis or ART, pretty much anything can work. The sound comes primarily from you and your instrument, not from the stuff you plug that instrument in to.