Scenario 1: DI & Cab
1st ch. Bass --> DI (Countryman/Radial) --> Console/Pre amp
2nd ch. DI --> Amp (Orange) --> Mic --> Console/Pre Amp
So then they are coming down say channel 1 & 2, then i blend the "clean" (di) & "dirty" (amp) to what i feel fits that particular song.
Scenario 2: Cab
1st ch. Bass --> Amp --> Mic (dark mic) --> Compressor --> Console/Pre amp
2nd ch. Bass --> Amp --> Mic (bright mic) --> Compressor --> Console/Pre amp
The idea being that if you balance the low frequencey and high frequeny microphones, you can get a more accurate representation of what the cab sounds like. I have used this technique a couple of times, after i read about it in an interview with Steve Albini.
Some mics i've used on the cab:
AKG D112, ATM 25, EV RE20, Beyer M-88
In addition to this, usually i'll compress at about 3:1/4:1 (3db), soft-knee, unless its slap bass than hard-knee.
Miking Cab Techniques. (Click on "stringed instruments" on the left, than E/gtrs/Bass up top)
Scenario 3: DI