The left, because you should be using https://colemakmods.github.io/mod-dh/

On QWERTY, capital ‘B’ should be typed with the left index while right pinky holds ‘shift’ key.

The relative frequency of the letter B is only 1.5%[1] so it doesn't really matter.

[1] https://en.wikipedia.org/wiki/Letter_frequency

Edit: Assuming English of course. But a cursory glance of other languages shows that the frequency is not much better, if at all. French 'B' has a frequency of only 0.9%; Finnish is the lowest at 0.2% and Turkish the highest at 2.8% - but still, relatively low. So why bother optimising for a letter you rarely use?

Yes, it should be typed with either the left or right hand.

But that's also kind of ableist, isn't it? It should be typed with whatever suits your particular use case. This holds as true even for people using two hands to use a QWERTY keyboard.