I'm listening to the Chris Stapleton recording right now, and it just sounds like an ordinary 1-2m-5 tune in 12/8. What do you mean "a bass part"? Any competent bass player can play the tune in 12/8. No need to reproduce the exact notes played on the record.
These bass players, are they playing the correct chords, and playing a simple spare 12/8 part? If so, then they're playing the tune.\
How do you think "the" recording came to be, anyway? Either Stapleton's bassist, who is probably an experienced professional bassist, came into the studio and played the part, no music, based on the chord progression and rhythmic feel, or a studio guy came in, played the part based on the chord progression and rhythmic feel. Do you really think that every single time Stapleton performs this tune, that his bass player plays the exact same notes at the exact same time?
It's folk music, everyone. It's derived from a combination of African-American practice and Scotch-Irish farmer/musician practice. You play what sounds and feels right at the time. Sometimes you play it faster, sometimes you play it slower; sometimes the bass player plays more busy, sometimes more spare.