The Bminor option does make a lot of sense (mel.net have discussed this in the past and not everyone agrees) but I don't think I've ever come across a factory box (in DG at least) that didn't have the Bmajor Chord. Many box players I know either tape over some, or all of the thirds or have the thirds taken out with a stop.

Mr Red, if the Bmajor sounds wrong try combining the B bass note with the D chord this, in effect, gives a Bm7 chord (BDF#A) and it works well as a compromise if you don't have a stop to take out the thirds and don't want to tape over the thirds either. This trick also works well to get Aminor - A bass note and the C chord (ACEG). I use these cheats all the time, they take a bit of getting your fingers and brain round, but well worth the effort. Other possibilities are there with combining different bass notes and chords but these are the two I use.