That's All Right had a B-side that was a cover of the song written in 1946 by which Bluegrass legend?
That's All Right:  Presley's version was recorded on July 5, 1954, and released on July 19, 1954 with "Blue Moon of Kentucky" as the B-side. Blue Moon of Kentucky: "Blue Moon of Kentucky" is a waltz written in 1946 by bluegrass musician Bill Monroe and recorded by his band, the Blue Grass Boys.
Bill Monroe