It could have just been a spirit who wanted to talk. Sometimes they die dramatically or have things that they still need to let out. It could have latched onto you if you went to somewhere old or historical. Once it saw you it saw a chance and took it. Though my answer is just based off from what I've heard before ^_^"
It wasn't an old building though lol It was my grand parents house (now my aunties and uncles)...Oh well...In that case I wish the spirit well...I've never forgetten them and I don't think I ever will lol They seemed ok :)
This could mean that you could be clairvoyant or just can see spirits, sometimes spirits will come to you if they know you can sense, feel or see them in anyway, they want to be able to talk to you and listen to you. But sometimes this can happen just about anyone. But you never know have you ever talked to you family about being a clairvoyant(medium) in your family, is anyone your family history ever had these events?
Just be glad it was not a dark figure. I have seen those and that is not a good sign. A white figure to me would seem to be some kind of guardian who wanted you to know that you were being watched and taken care of. I agree with a tramatic event happening and a spirit lingering because of it. It is usually a residual haunting-were they think they are still alive. I wish you well and blessed dreams. Just remember there are others out there-like me-to help you. As long as no harm has come to you or your family then I would not worry too much.