Absolutely do not plug the speaker out from your head into a DI box and plug the out from the DI box into your speaker cab!! The head expects the impedance that the speaker provides. The speaker expects the signal that the head provides. The DI box will change that relationship and most likely ruin your gear.
One does not record an amp with a DI box. One records an amp with a microphone. The DI box is for one of two things. 1) Converting the impedance of the direct signal from the bass so it matches what the mixer expects and so the bass sounds like a bass is supposed to sound when recorded direct. 2) Splitting the signal so the direct-from-bass signal can go to the amp and to another location with both at the proper impedance (your mixer for recording, the club's sound system, etc) at the same time.
Do this: Bass --> DI. DI --> mixer / DI --> Amp. Amp --> Microphone --> Mixer. If you want to record the amp and it needs to be quiet, just turn it down and turn the microphone gain on the mixer up, or boost the signal after it's been recorded. If your head has a recording out and you don't want to use a microphone, use the recording out instead of the microphone. The DI box in this situation is splitting the signal, sending one copy of it to the amp and one copy of it to the mixer--each at the proper impedance.
