What if, the duke's and Alice's idea of 'ghost' differ?
Right before the question, Alice was staring at, not the ghost, but the viewer, and when asked, deny seeing 'them'. Later on, she still deny seeing ghost, but admit to seeing the bride, which might implied that she can sense 'ghost'(the viewer), but can't see them, and is able to see the ghost bride perfectly, but put those in 2 different category. Also vaguely remember that there might be a fourth-wall break in like one the the witches chapters so the idea is not impossible.
that, or my caffeine-laden brain just went on a tangent.