Dennis,
My thought on the lyrics: When I read the lyrics I hear a slow country song as opposed to a faster, honkytonk song. Also, I'm not sure what you intended for the beat, meter and melody of the song. Based on the melody I hear in my head and the length of each line, I think you need more words that rhyme. You have the story line written out, so now you need to fit it to your melody while rhyming. Using the 4 lines to a verse pattern, you can rhyme either the last words in lines 1 and 2 and a different rhyme in lines 3 and 4, or you can rhyme lines 2 and 4. I rewrote verse 1 and 2 rhyming lines 2 and 4.
Sitting here alone at a Nashville bar
Listening to a sad Tanya Tucker song
Thinking about how my baby left me
After we've been together for so long
I don't know what happened no I can't explain
Can't help but wonder how she (he) could do me this way
I gave her my all, still it all slipped away
It wasn't enough to make her want to stay
Bartender pour me a shot of that homegrown whiskey
This one is for my baby who left me today
Pour me another shot of that homegrown whiskey
One last shot for a broken heart and bittersweet memories
Of course, these lyrics need to be tweaked to fit the melody of the song, but they give you a rough idea of what the line 2 and 4 rhymes sound like (although I think I rhymed all the end words in verse 2).
Here's verse 3 with a line 1 and 2 rhyme and line 3 and 4 rhyme:
Since you left me I've been going insane
Nothing I do seems to ease the pain
I can't stop thinking of you and how it could be
When you walked out of my life you took a piece of me
Two tools that will help you write lyrics are a rhyming dictionary and a thesaurus. You can find them both on-line. When I can't find a good rhyme for a word, I often go to the thesaurus to find another word with the same meaning and then look for a rhyme for that word.
Hope this helps.
Tim