Go straight from the Bass to the Computer
Record a track, then play this track out through the amp while recording it back in on another track.
Concentrate on playing while recording, concentrate on "sound" while re-amping.
Or you can record two or more tracks. One straight in for re-amping, and other tracks trying to capture sound. Watch the "phase" when you try to mix these. The mic and direct will always be off by a couple of ms. It shows up on clean digital recordings as combing.
Start with an Omni mic http://www.dpamicrophones.com/en/Mic...crophones.aspx
Start with the omni near where you think it sounds perfect to your ears when playing.