3-finger Single String - Blackberry Blossom A Section
This video briefly goes into Ryan Cavanaugh's technique using a common fiddle tune. While tabbing it out, I realized that my tendency is to play TITM, which I've heard is something Noam Pikelny does quite a bit, and Dennis Caplinger does as well.
I'm still working to figure out Ryan's style, but I'm not sure there really is a 100% accurate description of his technique. At this point, he probably just hears something in his head and plays it.
The more you experiment with different ways to play this melody, the easier it will be to use these techniques when improvising. For example, try starting the melody with your index finger instead of the thumb, and see where that takes you.