COULD COMPRESSION add to the problem ??
Of course it could. If you are running heavy compression on the kick with make up gain to match, then when the kick signal is not there the level of the background noise is elevated by the amount of your make up gain. If you are picking up some significant amount of bass guitar in your kick mic to begin with, this will just make the problem worse when the kick drum signal is not there.
Also, when you are experiencing crappy sounding bass or crappy sounding kick drum in the system, be sure to try the polarity inversion switch on your console. More often than I care to admit, when I'm having a tough time getting what I want to hear out of the bass guitar, it is because there is some weird cancellation or weird reinforcement thing going on. Hitting that polarity button will often suck the weird right out of it and things will straighten out and fly right.
Note that the polarity inversion button on your console may be incorrectly labeled as "phase" or use the phase symbol. Inverting the polarity DOES ABSOLUTELY NOTHING TO THE PHASE of the signal, rather it simply swaps pin 2 and pin 3 on the XLR, thus reversing the polarity of the input.