There is another Bb variant that is very useful all up and down the neck. It's really a Bb6 but can often be substituted for a boring old Bb with good effect. It's another pattern Merle Travis---and probably most Kentucky thumb pickers---used a lot; common in jazz too.

You barre the top four strings with your index finger as before, then catch the G on the bass E string with your thumb. That's the way Merle made it. Jazz players make the barre with their ring finger and catch the bass G note with the middle finger. In both cases, the fifth string is damped.

The thumbed fingering is really useful in the Raeger, Everly, Travis style because it gives you three unused noting fingers that can find melody or harmony notes as needed.

If the major sixth just won't fit, you can slide your thumb one fret north and play it as a Bb7.

Extra credit.
Here's an interesting little piece of theory. If you make the Bb6 I describe the way the jazz players do---ring and middle fingers, no thumb---you can slide your four-note barre back to a three note barre, exposing the D string, and catch E on the D string with your index finger. This has the effect of flatting the 3rd tone of the Bb scale turning the chord into a Bb-6 (minor 6th). Most of you will recognize this as a chord you often play and refer to as C9. It turns out a Bb-6 and a C9 have the same notes just like C and A-.

Along the same lines, the Bb6 pattern across the third fret---thumbed or fingered---may also be called G-7.

Go figure.

- Mark