The only recording I can find online of BREAD AND GRAVY (not the Hoagy Carmichael song) is by J. E. Mainer's Mountaineers. It sounds like a rather late recording. It's on the Various Artists compilation "Sound Traditions: Appalachian Mountain Bluegrass," Rural Rhythm CD 317, 2007. This is what I hear in a sound sample found at Allmusic.com:

…we used to eat liver and onions.
But beef stew we never went wrong;
But lately I've noticed the difference,
And that's why I'm singing this song:
On Monday we have bread and gravy.
On Tuesday it's gravy and bread.
On Wednesday and Thursday …

[There's enough there to get an idea of the tune, and it's nothing like "Rosin the Beau."]

https://www.youtube.com/watch?v=86HWQQzoL9c