My small experience with seeing a ghost was that it appeared out of a mist. The white sheet could be a figurative way of portraying that. But there was a face too, and that stood out most starkly. And the gaze, when it fell on me, was electrically frightening.
I was probably 2 years old and was fussing loudly in the middle of the night, when a kind lady came through a door and walked over to me and hushed me down. She was in a blue ball gown-like dress. The next morning, I remember looking at the part of the room where she came out of, and there was no door there. Years later, my sibs told me that house was haunted af. I’ve spent my life trying to rationalize this experience.
I have vivid nighttime hallucinations. Sometimes it is bugs or spiders (so many spiders), other times dancing teacups emptying themselves onto my face. I remember a time when my alarm clock was a lion that I had to tame. But a few times it was very much what you describe. In one case, a ghostly looking woman looked me directly in the face from not more than an inch away.
Our minds get kind of funny when we are asleep. They manifest strange and incomprehensible imagery. I wouldn’t make too much of it.
(By the way, I have these much more frequently when I am stressed. Perhaps that was a factor for you?)