Low Level Noise in Logic X

I'm trying to remove low level noise from a track in logic X. I've experimented quite a bit but remain baffled. Here's the scenario:

the project has a single live guitar track, output directly to the Stereo bus. No sends/busses.

there are no plugins in the project, other than Noise Gate and Soundsoap

with the plugins switched off (and when removed), noise is present before, during and after the note.

with soundsoap turned on, the noise is reduced but is not reduced to zero....so still remains present before, during and after the note.

When noise gate is added, the noise is removed before and after the note, but, as expected, doesn't remove noise on the note itself.

So I can't seem to be able to trap this persistent noise and remove it, without reducing the track output to zero, which of course means there's no sound at all!

I've tried adding Soundsoap & Noise Gate to the Stereo Bus as well, doesn't make any difference.

the noise is not present if Logic is not playing

the guitar is a Fender Precision Bass, played through an Apogee Duet into the Mac/Logic. I get similar noise issues with direct input recordings from other guitars (e.g. Strat)

So I'm baffled as to where exactly this noise is coming from and how to remove it?? Any help appreciated.