I use a US Fender P Bass and a blend of DI through a UA 6176, tech21 sansamp hardware and the Waves CLA bass plugin. I make sure all three tracks are in phase. You can get a wide range of bass sounds with different balances of all three. Sometimes I'll use a IK precision compressor on the bass bus in the mix. I have also used melodyne on occasion to fine tune a bass track.

You should check out Overload Mark Bass.. Awesome Bass Amp sim.

I go direct into sound card with my Musicman Stingray, don't use and amp sim, just some compression and EQ in prochannel and am getting great results.

Fingered parts at beginning and end ... slap in the middle.

https://soundcloud.com/steve_karl/water-lilies

Another option if the DI thing isn't what you want is to buy or build an isobox.
You can have that amp sound, with te speaker you want and mic(s) you want.
 
I have been using IR's, sims, etc. to record silently and while they sound good, they just don't have MY amp tone. I don't really have an issue with sound levels I just prefer my neighbors not hear what I'm doing and was keeping my amp at a bedroom level. That doesn't really let the full tone out of a 100w tube amp. Now I can crank it, barely hear it and record the guitar with excellent results.

Yet another option - DI the bass through a bass pre-amp such as one of the MXR or Sansamp ones. I've used an MXR one for years and it adds warmth and punch in a way I find much harder to get with digital/software amp sims.

Like others above, I'm in the simplicity category - cheap Rogue bass direct into a Focusrite 18i6.  I've used my fair share of amp sims, but for my last few tunes I've stuck mostly with EQ and compression.  Quite simple, but in the context of a mix it seems work. 
 
Songs using the above are in my sig if you're interested.

If the OP is looking for a straight DI bass recording, a higher-end preamp is a god-send.
I've had 101 different devices for recording electric bass.
For straight DI, nothing has made it as easy as the Neve Poritco II. 
Plug-in a decent bass... and the sound straight off the preamp is awesome.
Not cheap... but it's like getting a gear upgrade across all your mics and instruments.
 
If you're looking for more of an "amp'd up" type sound, checkout the Helix LT.
Helix is great for recording guitar and bass.
Has nice impedance appropriate input, 123dB dynamic range on the A/D, great amp & effects, and functions as an audio interface.
 
 

stevec
or my last few tunes I've stuck mostly with EQ and compression.  Quite simple, but in the context of a mix it seems work. 

 
Countless good bass recordings have been made that way - live sound is often done the same way, with the bass split by a DI box before the stage amp.
 

I record almost every Bass track in to an outboard compressor first (just light compression to tame the transients).
That goes directly in to DI in to my Focusrite mic pres.
I typically double every stringed bass track with a synth of some sort to fatten up the sound.
its time consuming but once you have done it 20-30 times it becomes easy because you know the note values you are looking for.
Adding saturation and compression are a must for any bass track.
I have never found any benefits from recording bass with a mic unless the room was good and the amp was good.

I'm the same as most and DI. and have pretty much tried everything except high end pre's. I use various Ibanez bass's I've collected and a US P bass. Every time I like a bass on something I can check on, the bass used was an old, real, P bass. Just goes to show......
 
I DI, to my scarlett. and line out to a Behringer combo for feel, and my fav in Amplitube is the Trace Elliot head, but I use a lot of different ones. I've miked and recorded both direct and cab on many occasions, but have never used the cab track in the mix, so I no longer bother. I do for some guitar work however, to get extra bottoms into the mix, but for bass you can add your bass audio source to midi, and synth your way to achieve what your looking for if your after something different.
 
While talking different, my basses are all shod different. Flat stainless, heavy round wound and light round wound, and I have a fair collection of strings in the box that I can change over. If you buy good strings and keep them clean, they can last for ages. I've had one set of flat wounds since the 80's, and they gigged 5 days a week for quite some time. They are retired, but I still put them on every now and then when looking for a wooden, upright sound.
 
So many options hey. But the general flow from this thread is record direct, clean, good bass, spending what you can afford. Can't go wrong really.