I've never been a fan of country music but lately I've been wanting to try playing different genres. I mainly play stuff like RATM, Nirvana, Foo Fighters, etc. I'm looking for some Country songs that don't have just 3 notes played over and over, but something that would actually have a fun groove to it. Recommendations?
Well It doesn't really count but country music (a night in hell) by Stuart Hamm is cool.

I would look into some of Waylon Jennings stuff. He got his start playing bass for Chuck Berry so he kept the bass in his songs when he went off on his own a little more interesting.
I know it's technically bluegrass, but duelling banjos. Foggy mountain breakdown also has a pretty badass bass to it.
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I've heard my grandma mention Waylon Jennings a lot. Since he was a bass player first I'll definitely check him out. This should be interesting.
Use scales, and work out your own walking bass lines. Country isn't really known for flashy bass lines, just underpinning the drums and lead guitar, so if you want flash, make your own.

Take some simple progressions, and try and make the bass a little more intricate and melodic, while keeping a sort of root-fith feel, with notes in between, like bluegrass guitar pieces.
Expand your search to bluegrass, folk and rockabilly. They have a lot in common with country, and you'll find flashier bass lines.

Look up the bassist, Jack Casady.
"Punk Rock should mean freedom, liking and accepting anything that you like, as sloppy as you want, as long as it's good and has passion."
Check out songs that feature Michael Rhodes, Bob Moore or Michael Pomeroy. Bob Moore is one of the pioneers of country bass playing. Most people concentrate on his work with Elvis but he did backup chores for a slew of people in country music over the years.