Hi,
I think Joeydavidson makes some fantastic points - adjusting your compressor to above unity (to taste, in relation to the GK natural overdrive) is a great way to get your sound.
I would reccommend using pedal comp's as opposed to rack ones with GK amps - this way you can use them to drive the input on the amp, AND you can use your eq to characterise the comp'ed sound instead of visa-versa.
The comp I use (mostly for live shows) is the DOD Milk-Box - it really fills out your sound, and is much, much smoother than any other pedal I've tried...MXR's, Keeley's, Aphex, BBE, Boss, as well as many other 'one-off' boutique pedals.
Second in line are other pedals such as the Markbass Compressore, Ross, Focusrite and some others. All in all it boils down to taste, so check 'em all out if you have to haha!
As a great alternative, visit
Compressor Reviews for some GREAT insight into the world of compression on bass.
All the best! JOHN