The Scottish tune 'Jimmy Allen' is in D, but utilizes a Bmaj
chord in passing.

The Morris tune 'Princess Royal' also can make very good use
of a Bmaj when it is played in the key of G, as it usually is.

I particularly appreciate the stop on my Salterelle Nuage which
cuts all of the bass thirds out.

As mentioned above, one strategically placed piece of tape will
silence the 3rd in the Bmaj chord, making it nicely ambiguous.