Nashville isn't like Chicago, where you'll hit bad traffic at 2:00 in the morning. It's just predictably bad at the expected times of the day. (And, to be fair, I think they've been doing construction for a while on 65 north of town, which has caused some permanent tie ups.) So if you can get through town between 10:00 a.m. and 2:30 p.m., you shouldn't have any problems.
Barring that, if I were coming from Bowling Green, and were desperate to avoid Nashville, I would probably cut from 65 over to Gallatin via TN 109 or TN 25, or perhaps take the scenic route all the way via US 231, and link up with the northeastern terminus of I-840, swing 840 down to 65 way south of Nashville, and be on my way.