The Doctor does explain why using the Tardis would not work. As close as they are to the black hole it would be impossible to pilot or land anywhere else on the ship with any accuracy, while the time differentials would simultaneously allow the Cybermen eons in which to evolve excellent plans to stop and/or destroy them in the attempt.
There is no reason not to return to the bridge at any time. While this would involve dropping into the slower time near the black-hole this is irrelevant as there's a time machine at the destination. They can simply offset any lost time using the Tardis. There's nothing to prevent a complete evacuation of the entire ship this way.
There is no reason not to return to the bridge at any time. While this would involve dropping into the slower time near the black-hole this is irrelevant as there's a time machine at the destination. They can simply offset any lost time using the Tardis. There's nothing to prevent a complete evacuation of the entire ship this way.
Some of the shots in the woods (around 38 minutes) show the Cybermen walking slowly but the accompanying sounds are for them marching at a much faster pace.
The lifts could never pull away from the black hole (towards the Cybermen) as they would have to move against the same gravity that was holding the ship there.
Missy tells The Master he doesn't remember meeting her because their timelines are out of synch. Yet she is able to obtain the spare TARDIS part by recounting the meeting between them, which he has already said he doesn't remember.
Once The Doctor realises a black hole is slowing time at the bridge end of the ship he could simply use the Tardis to fly to the other end and arrive as Bill leaves the lift saving a lot of trouble. Missy should also realise this immediately as well.