The State DEPARTMENT works for Bush too. Are they following his orders or do they operate independently and contrary to Bush's policies?
No - they do not follow his orders and yes they operate independently and contrary to Bush's policies.
You have obviously never worked with a bureaucracy before. They cannot be controlled. Presidents and Secretary of States come and go - but the lifer employees go on and on. It is next to impossible to change a bureaucracy. You can't just go in and "clean house":
Number one - these are union employees, it is extremely difficult to fire one of them. It takes a tremendous amount of time and at arbitration, the employee almost always gets their job back (with back pay to boot).
Number 2 - someone is always needed to do the day to day work. You can't go in and fire thousands of people at once (even if you could). The bureaucrats know this all too well - that is how they can continue to ignore the President's policy.
I know this from personal experience working with a state government department. Directors came and went, governors came and went - but the bureaucrats are there forever - and they know that fact very well.
What makes it even tougher for Rice and Bush is that the State Department was packed full of Clintonistas during the 90s.
It sounds so easy - "just get rid of them". The phrase "Easier said than done" was never more apropos. It's an impossible task.