Heh, the first scenario is straight forward. BA has the right to set its a drress code.
With the teacher there are a couple of things:
This isn't true, Islam does not dictate the wearing of a veil. In practice its basically up to the individual woman if she wears the veil.
I think face to face contact is incredibly important when teaching and just conversing in general. IMO it does create a barrier and concealing ones face always creates an air of distrust. The womans caveat of wearing it in front of male colleagues only is hypocritical nonsense since she already removed it once for an interview with a male governor of the school.