The B stands for...
The Software Alliance is the renamed Business Software Association, and its formal brand is now "BSA | The Software Alliance". Like, the B doesn't stand for anything at all.
I suggest we reconn it to stand for "Beta", which nicely describes both the Association and the Software for which it stands.
I also suggest we write it as βSA, just to annoy their marketing people. (I know, that's a lowercase beta, but the uppercase one only works as a joke if you check the encoding. Dratted homoglyphs.)