>One line went something like, “but you don’t know meeeee….but you don’t know me.” It is a jazz song maybe by Eartha Kitt, Ella Fitzgerald or Sarah Vaughan. From back in the forties, I think.
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>Anyone know this? I'm trying to find the song name and lyrics for a friend, but almost all lyric sites are blocked here at Headquarters 1984.

I don't know if it's the one you want, but I know that Ray Charles did a song called "You Don't Know Me" back in the 50's. It began:

You give your hand to me
And then you say, "Hello."
And I can hardly speak,
My heart is beating so.
And anyone can tell
You think you know me well.
Well, you don't know me.

Like everything else he did, it was a terrific song.