Although I got it correct, from the research I have done, no-one really knows what the B stands for.
It is never clearly defined by anyone.
One article I found has some some interesting tid bits of info about it 🙂
"But in the paper that Mr. Bayer et al wrote introducing this structure, they never defined for us what the ‘B' stood for, so nobody knows for certain if it has a meaning."
Bayer being one of the team who developed the B-tree.
Of course, if anyone has later info from the team where they did indeed qualify what it means, please share 🙂