Bezier Spline Alignment Issue

Hey!
I need to do some scripted animation using Bezier-Curves. I managed to move a ball along the curve (A) and now i need some kind of inverted version where the ball is static and the curve is moving through the ball (B) like shown in the attached image. Im sure there must be a clean solution but i already spent too much time without a solution.

Can anyone give me a hint how to acheive that with just the given position of the ball?

Its more of a math problem, but maybe someone can help. Thanks!

This idea is relatively tricky, but attaching your camera as a child of your ball should visualize your animation perfectly if there is not many restrains in your project.

Thanks for your answer!
After some trial and error i found a way to achieve something acceptable. The basic trick is to invert the Z-Axis (which ist the forward direction of my beziercurve alignment) and invert the rotation using Quaternion.Inverse.

I use it to move generated landscape along a stationary camera, so your idea may work in other cases.