"Country" I think, has a pretty even tone throughout generally. Try using your parametric EQ to dial out the muddy notes. To my ears, the G and A on the E string tend to bring the most mud. Try fretting those notes to remove the muddiness overall. To do that, dial the Para EQ gain down -15 db, fret the G and turn the frequency knob around different directions till you get the boominess out without making the sound too thin. Then dial the gain up a bit, do the same thing, until you get it more or less the way you want.
Leave the low bass relatively flat and dial out some treble. For that kind of music, you don't (read: I don't) want any squeaking and grinding on the strings, treble wise. As was mentioned before, you basically (no pun intended) want to get rid of the boominess and too much sizzle, but you still want a good presence.
Really, though tone is so subjective, it's tough to give any real advice as to what YOU actually want. It depends on the bass you use, the strings you use, the way you play, etc, etc, etc... Plus the way it sounds once you dial it in at home is liable to change a good deal on the gig, so you'll need to know what you want to sound like in order to make it happen anywhere you go.
If you're fiddling with knobs at every song, then you don't know what you want to sound like. Plus if people want you to change your tone, there is no way for them to describe what to change because you're always making it different. Being consistent goes a long way and is easier on you at the gig.
But you haven't been playing that long and finding your tone may take awhile. I was talking to one bassist on the break of one of his gigs and complemented him on his sound (plus he was an awesome player) and he told me he'd been looking for that sound for 30 years.
