It's been a while since I've seen the film, but I remember snorting and huffing at virtually all the Alexander Palace sets. They struck me as completely made-up. It's not entirely fair of me to criticize, though -- in the early 1970's information about the palace's interior was probably not readily accessible to westerners the way it is now.
I don't recall the bedroom specifically, but as for the walk from the personal quarters to the palace entrance? I don't think such a walk existed. The entrance to the property is to the left of the palace -- you can see a car on the public street at the left, and just make out the private lane leading to the palace through the trees:
That private lane leads directly across the front of the building, which means Nicholas and Alexandra could have been dropped literally at their own doorstep at the end of the left-hand wing. Once inside, they were already *in* the private wing. There is a central corridor, but my impression is that it was used primarily by servants; the imperial family's private rooms interconnected, and neither the imperial bedroom nor the mauve boudoir communicated with the corridor at all. Here's a photo of the actual AP corridor as it appears now:
The upstairs was laid out similarly. Here are the floorplans:
According to these plans, the curved open stairways portrayed in the film did not exist, either.