The book solution is intuitive because it shows that if a blue ball reaches the bottom, no further logic is required to determine that a red ball should be intercepted, and so there is a direct route from the red chute to the interceptor.
However, by the same logic, if a blue ball makes it to the bottom, that means Bit A started out pointing to the right, and is now pointing left. Knowing this, we can use Bit A in the red ball path, which saves us one green ramp.