Better Recording Options for Bass Covers?

[rydin4lifebass]

I currently record some bass covers using this signal chain:

Bass > Zoom B3 > Fender Rumble Amp xlr out> Tascamp DP-008 xlr in

I then upload the resulting bass tracks into Audacity and try to get a decent mix along with the original track. Would it be beneficial to record the bass directly into my computer using a DI box? I have no real reason to switch other than wondering if it would provide better sound quality. I've considered this, but I'm unclear on how I would get the same effects and amp modeling that I can using the Zoom B3 unit. Would that just be Bass > DI box > Computer ? Or..would it be better to just plug the Zoom B3 directly into my computer to record?

These are my two most recent attempts. I thought I heard some slight ringing or unwanted tones in the isolated bass tracks,but listening back I don't really hear them. I suppose this could be the quality of the headphones or speakers playing it back and trying to reproduce those sounds? If anyone does hear it, are there any tips to reduce some unwanted sounds?

Thoughts on these as far as sound quality goes?

Cake - Friend is a Four Letter Word (Bass starts at 0:38)
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Marilyn Manson - I Put a Spell On You (Bass starts at 0:12)
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[Badwater]

You're on the right track. If you want the FX of the B3, eliminate Bass> B3> Interface> computer DAW. This eliminates the variables of the amp and DI box. And if you're not getting the results you seek on the Tascam, the next step up is a Interface and DAW. Depending on the DAW, it will be easier to record, mix, and establish presets for many recordings to come. The cons of a DAW are: not as portable as the Tascam.