Well actually, most of her body is covered with the suit. The only skin showing is around her mouth.
Yes, the most important part of person recognition ... the face.
It would be a rare person to see both and make any connection - assuming they even notice when she's in the suit.
She has white skin and wearing a black suit. Can't get more contrast than that.
White skin
Again, all I am saying is if she were smart, she would not show such a rare feature to the world. Its like if she only had one arm, villains would be -
"Hey, who is that hero with one arm? If we want to know, lets start by looking for a one armed person and see where that leads"
I see Batwoman swinging around and the next day I am at a coffee shop and see a white skinned woman walk in, guess what I am thinking?