I'd like to answer as far as buckets are concerned but leave the CMBR to a cosmologist or a real relativity-ist. Mopping the floor up after the chaos left by my children, I think of myself as an expert on the former!
In GR it is immaterial whether one describes a "force" as an "inertial force" or a gravitational field. All one "knows" is whether one is accelerated relative to an inertial frame: more fully: suppose one carries a "reference frame" with oneself (imagine a set of straight measuring rods representing the $x, y, z$ axes. Then this system of rods is an "inertial frame" iff all of its points move along spacetime geodesics as defined by the Einstein field equations. This can be worded more technically: the co-ordinate's sytem's origin follows a spacetime geodesic in the manifold and the spacetime manifold tangent vectors represented by each rod are Lie dragged by the system of geodesics.
A point on your bucket's rotational axis may well move along a geodesic, but there is, in GR, an "absolute" notion of rotation insofar that one could detect rotation with respect to the system of rods I described above. So all points on the rotation axes follow geodesics, but molecules of water away from the axis follow helices relative to the geodesics swept out by each point on our measuring rods.
Think of GR as an "application note" to go with Newton's and Euler's first and second laws. GR tells us what the inertial frames are: i.e. the definition of when and where Newton's first law and its rotational analogue apply. Then we apply Newton's and Euler's second laws (locally) to deduce all motion relative to these inertial frames: acceleration is then what we measure with an accelerometer. Whether we sit stationary relative to the surface of the Earth or accelerate uniformly in deep space at $g$ metres per second has the same physical description from this standpoint. Note that spacetime has to be locally flat, i.e. Minkowskian over the scale of the description of the accelerated motion for this way of thinking to apply (as it will be if we consider small enough "chunks" or "stages" of the motion): we can think of this description as applying in the tangent space to the spacetime manifold. In general, we'd have to update our inertial frame and reapply this thinking repeatedly if we follow an accelerated motion over longer scales in spacetime: this is what I meant by "applying locally".
Weird though it may be, if two spaceships met in deep space and were spinning relative to one another, from a wholly kinematic standpoint, we couldn't say which were rotating and which were not. But GR does not agree with this: one spaceship can be still relative to the Lie-dragged co-ordinates and so those riding in it will not feel a force and be in freefall with their lunch and coffee floating around them! Acceleration in GR is, in the sense (IMO the only one that matters) of what a system of accelerometers will tell us, absolute. See Mark Eichenlaub's wonderful answer here for more. I think this is likely what Lionel's answer meant about deep rabbit holes and Mach's principle - but, hey, you should follow Alice, drink all the bottles you find and look it up. Mach's principle, as far as I understand, tells against Einstein's general relativity and recently is being found to gainsay the observed results of gravity probe B (see Wiki page) so it is now falsified where GR is not, but it's thoroughly interesting from an historical perspective and from the standpoint of getting into the head of a very bright and altogether originally-thinking person (Ernst Mach).
Interestingly, the Lie dragging condition this is another way of saying that the torsion is nought in GR: other gravitational theories (which I know nothing of) such as Einstein-Cartan theory have nonzero torsion in some conditions although I believe in deep "empty" space there is still no torsion.