"Nieto" is a grandson (and "Nieta" presumably a granddaughter).
"Bisnieto" is a great-grandson (and "bisnieta" no doubt a great-granddaughter).
"Bis" means "encore".
So is a grandchild an "encore" grandchild?
I think of an "encore" that a musical band may perform as a sort of a "bonus" set (one ore more "extra" songs to finish a concert, if all has gone well, or to reward an appreciative audience).
Is the sense of "bisnieto" that, although one may expect to have children and grandchildren - nothing too unusual in that - to have great-grandchildren is something of a "bonus"?