Need some advice

Logic has a IR Loader called Space Designer. It's a reverb plugin but it has some IR cabinet model presets of either recorded impulse response files or synthesized impulse responses. It has a whole bunch of parameters to edit the samples. Could help with what you're talking about.

 

Remove the amp from the chain, plug the bass right into the interface. Is it cleaner?

 

Let’s hear a sample. I understand the concept of “air”, but it can be a vague characterization which an actual sound file might help s understand and possibly suggest a solution.

 

I'm guessing this "air" is what others might describe as "hiss". It's common in amp DIs. I haven't used this Eden head before so I could be wrong.

A low pass filter at 10k (or lower depending on if you're slapping and tapping or not) should help. If you're not slapping or tapping, go lower...

 

this A/B test will help you determine the cause/source, OP. i know that a lot of cowboys want to record with all the 'guns' they can get, but if you want deliberate "quiet" and/or the cleanest signal to tape/drive possible = go direct. good luck with your recordings!