Bass is tricky! For old jazz and oldies rock, its not too hard, but today's modern slap n pop n funk piano-ey spanky heavy bass tones are no easy task!
For most albums I do, I have the bass player go buy some lite strings....and a LOT of them. This is for recording NOT live, so take the scowls off your faces

Buy LOTS of extra "A" strings " if the store will sell them that way.
We'll put on the new strings exept that the normal " E" string is thrown out and replaced with another " A " string. The intonation will immediately suffer, so you gotta keep messing with that truss rod when you do this. Also there's a danger of the neck actually twisting. The sonic benefits are worth it tho if this is the sound you're after.
Change the "E" and " A" strings after every 5 to 10 minutes of playing if you want to keep the " zing thing " change the others every few hours as well, and KEEP checking the intonation.
Be careful that the pickup bobbins arent messing up your sound or string behaviour also
I like to both record a Direct sund AND get " moving air " from an amp and cabinet at the same time.
I like to use direct boxes that split the signal so I can get a clear sound in the DI and whatever processors the bass player likes, going to the amp.
I perfer passive DI's with Jensen transformers
very very easy and cheap to build a world class DI box right here :
http://www.jensen-transformers.com/as/as066.pdf
Usually for the cabinet Ill just use whatever mic seems good for a kick drum;
akg d-12 or d-112,
Audiotechnica ATM 25, EV RE-20,
sure beta 52 ( my current favorite! ), or nuemann fet 47
move it around till it sounds good and there you go
at this stage for an oldies rock or jazz sound, I will filter off at the mic pre pretty much everything above 3k. For modern sounds I will try not to eq at all at this point, but I will mess with the EQ and see whether or not it WILL make the sound I think i might be after, but then turn the EQ off.
If you are track count limited, and need to summ both DI and mic to one track, now is the time to experiment with phase. MAKE SURE the two are in phase, they most likely WONT be. while the bass is playing, move the cabinet mic back and forth until you find the point where the summed signals are the loudest.
For dynamic compression at this stage, Ill usually leave the amp signal alone, but I may throw a normally NASTY limiter on the DI, just to make sure there arent many digital overs...if its going to analog, dont even worry about it...unless you dont have enough compressors to use later.
When it comes to mix time, Ill use delays and such to line up the DI and mic signals into phase or move the trakcs relative to one another in a DAW.
EQ'ing and compressing, I like to think of the DI signal as carrying the information, the words you got to say, while the cabinet signal tells you how loud you are saying them, what you are feeling about these words. The DI will contain lots of nice hi's and lows, and maybe a little too much movement, so some compression is prolly in order. The amp signal can get by without usually.
Ok so now you say " alright damn my bass sounds good, but OH NO, now it is fighting with the kick drum and the whole mix is a muddy mess"
no problem, you got a tool for that
take a split from your kickdrum track at the patchbay or wherever.
Plug this into a compressor's SIDECHAIN input.
plug the bass track(s) thru the compressor's normal audio path.
Make sure your comp is in sidechain mode. Start with a ratio of around 6:1. SUPER FAST attack, and around 80 Ms release.
The trick here is to make it so that the bass " ducks " everytime the kick drum hits, so they are not fighting for the same sfrequencies at the same time. Also the added benefit is, it now will sound like the kick drum is " playing " the bass. You KNOW the sound, you've heard it a million times...Keep messing with the attack and release till you can get it to sound somewhat natural.
Aaron Carey
StudioZ/Pipelineaudio
www.studiozpro.com