My understanding is that in the case of an extremely massive object, frame dragging leads to local changes in spacetime that amount to "changing" what the "back

My understanding is that in the case of an extremely massive object, frame dragging leads to local changes in spacetime that amount to "changing" what the "background" reference frame looks like? If the bucket were truly massive it would indeed start to look a little bit like space were rotating around the bucket, and not the other way around? Since the bucket is of negligible mass, of course, it is the mass of the rest of the universe that "sets" the reference frame. This is my layperson's understanding. For me the important point is that it is the global arrangement of mass in the universe that determines the reference frame. Conceptually, I find it helpful to think that, indeed, you can make the universe spin around the bucket, if your bucket contains a fair portion of the mass in the universe? Perhaps I have misunderstood something, however.