A lot depends on how much compression you're using, the type of compressor and how it's set. You can have everything from just peak limiting to a varying amount of compression affecting every note.
I like compression that fattens/fills out the tone a bit, but doesn't squash every note and kill dynamics. The Aguilar TLC and Diamond Bass Compressor work well for me when used in small doses. I don't use compression often, but when I do it's almost always as a tone shaping/voicing effect and not for volume control.