Mix buss compression and other tweaks during the mastering stage are another part of what gives the bass (and entire track for that matter) that professional sound that you may be looking for.

soundtweaker
If you want an Ampeg B15 type sound from a DI and you can afford it, get the REDDI DI.
http://www.sweetwater.com/store/detail/REDDI/
For a clean transparent tone get a Countryman DI.
http://www.sweetwater.com/store/detail/DT85/
If you want a preamp that oozes vintage goodness try a custom made CAPI VP28
http://www.customanalogservices.com/vp28
 
There's a ton of great compressors out there. Pete's Audio BAC500 is one of my fav's for bass.
http://petesplaceaudio.com/bac-500.html
 

 
My preferred way to record bass is to go direct using a quality active DI then season with EQ/compression as appropriate.  Never had a client complain about the recorded result (about having more bass in headphone mix - yes).
 
 
Been awhile since I compared DI's.
But when I was a recording engineer (back in the 80/90s) I compared quite a number of them and there was no question that active DI's sounded better than their passive counterparts (cleaner, punchier, more transparent). My favorite was the Countryman type 85 DI - I ended up buying one just to insure that I had at least one decent DI on hand if working in an unfamiliar studio.
 
 

Hey Jim Roseberry -- Question about the Zoom B3 : Can it be made to output a clean (unprocessed) signal on one output and the full Bass Amp w/Cabinet Sim on the other output, simulataneously? I downloaded the B3 manual, but it wasn't entirely clear on that. The connection diagram shows one of the 1/4" outputs connected to a Bass Amp (which sort of implies the 1/4" output is clean to start with). The diagram also shows that there is a switch to set the XLR output to Pre or Post (Clean or Processed). So if you want both clean and processed outputs would you use the XLR for processed and the 1/4" for clean?

Actually that is a good point. I do know with the bass pod pro you can send two outputs to your DAW, one with the amp sound and one clean DI sound. Then once recorded you can mix them to taste or add another bass sim onto the clean signal for some additional color. The cheaper grey bass pod bean should have this option as well. I don't have mine setting in front of me right now so I can't say for sure. If the OP is interested a google search should give the answer easy enough. I myself have no idea about the zoom b3 though.

rodreb
Thanks for all the great advice everyone! What started this is, I watched the recent Pensado's Place with Tchad Blake. In it, he said he hasn't mic'd up a bass amp for years. He records all his basses direct in thru a Sansamp Bass Direct. In fact, he sang the praises of his Sansamp highly!
So, I thought, "I'll buy me one of those". Then, I decided to see what other folks are using so, I made this post.
Bottom line, I'm looking for a direct recorded bass sound that sounds well recorded/produced.
Typically, I record bluesy rock/indie/alt stuff.
I've tried the high impedance D.I. inputs on Focusrite ISA One and Presonus Eureka, and an ART MPA Pro II, as well as a plain old direct box from ART. I've also tried it plugged right into my Yamaha RM-800 mixer. Any/all of these are not 'BAD". I would just like to find something that gives an already produced sound without having to add a bunch of additional compression, EQ, etc. I suppose I could just record a dry, D.I. then add and amp sim after the fact but, would rather get it all in one shot, on the way in, with no latency to have to deal with.
As far as the players I record, I'd say I've been very fortunate to only have players in the very good to excellent range (so far).

Some of the greatest records were recorded using DI bass. Granted, a great preamp helps. 

I use Tech 21's (same company that makes your Sansamp) VT Bass. It is very versatile. It's my go thing for bass. In fact, it's one less thing I have to think about how to record. I roll off some bass while recording. A nice midrange tone is easier for me to work with. Adding more bottom is easier that taking it away.

I put the bass direct into my ART pro MPa II pre.  It sounds great.  Sometimes to get a bit more grit for aggressive songs, I'll patch in camel crusher (a great plug for bass...and it's free).
 
That and a bit of compression always delivers a great sound.
 

Hi Guys,
 
lots of great responses here. To throw another DI into the mix... I just picked up an Eden WTDI from Sweetwater for 150 bucks.  Its basically an Eden preamp in a stomp box.
 
It has knobs for: bass, mid, treble, gain, master  and a one knob compressor
 
it also has an "enhance" knob which seems scoop the mids to various degrees. (eden cabinets get a little midrange barky when cranked up and this seems to compensate nicely)
 
it also has buttons for ground lift, bass boost, midrange shift.
 
Finally it has one input, one unbalanced output and one balanced XLR output.
 
It sounds really nice plugged in and recorded even without an amp sim.

bbdude
Hey Jim Roseberry -- Question about the Zoom B3 : Can it be made to output a clean (unprocessed) signal on one output and the full Bass Amp w/Cabinet Sim on the other output, simulataneously? I downloaded the B3 manual, but it wasn't entirely clear on that. The connection diagram shows one of the 1/4" outputs connected to a Bass Amp (which sort of implies the 1/4" output is clean to start with). The diagram also shows that there is a switch to set the XLR output to Pre or Post (Clean or Processed). So if you want both clean and processed outputs would you use the XLR for processed and the 1/4" for clean?

 
Yes, you can manually switch the XLR to provide a straight (unprocessed) DI sound... while running the AmpSim via the 1/4" output/s.
 
The Bassman 300 model in the B3 easily bests any other bass amp model I've heard (including all the POD units, Bass V-Amp, software AmpSims, etc).  It sounds extremely good even when compared to (well recorded) tracks thru an Ampeg SVT Classic.  If you want a quick/easy means to to record an "Amped Up" electric bass track, the Zoom B3 is stellar.  At $200, it's a steal...
 
Tip:
Put the DynaComp right before the Bassman 300.

jmasno5
I use Tech 21's (same company that makes your Sansamp) VT Bass. It is very versatile. It's my go thing for bass. In fact, it's one less thing I have to think about how to record. I roll off some bass while recording. A nice midrange tone is easier for me to work with. Adding more bottom is easier that taking it away.

I just got the VT-Bass Deluxe.
If you're running straight into your audio interface (not running the SansAmp into your bass amp), the VT-Bass sounds considerably better than previous SansAmp units.  You can dial out that high-end string "clack" and the mids are much better defined than the BDDI, RBI, and RPM units.
 
I'd describe the VT-Bass (tonally) as somewhere between a straight DI and a full-on "Amped Up" sound.
Good unit if you want a tone that's pretty well "finished" going in... but is still neutral enough to send thru an AmpSim plugin.  Super convenient and affordable...