Thanks all. I am going to have to locate a copy of The Innocents and see if it is the move.
If the lady/ghost is seen in the lake, it is probably the movie. I do believe this film is too recent as I first remember seeing it when I was very young which would put it before 1961.
All that aside, thanks for the input and if anyone else has another movie, please list it for me. This is driving me bonkers.