Isn't there another formulation of BB where we count shifts (from left to right, and from right to left) a TM makes instead of strings of contiguous 1s. I remember seeing a video about this definition.
The variant of BB discussed in the article is counting steps, not 1s. (I guess "shifts" is equivalent to steps, although that seems like a more roundabout way of specifying it.) Also, I don't think anyone counts strings of contiguous 1s, although of course one could define such a thing.