I don’t know what she might be thinking, only she does. To me, she deterred your facebook request and left you no phone number to pursue friendship after their moving. In other words, the friendship is to not be continued in her mind. She said ‘sure, okay’ when put on the spot, but didn’t mean it. It may be because she is a married woman and you are male so she doesn’t feel it’s appropriate to pursue this friendship.

Since she moved and you have lost touch, it doesn’t matter that you sent her the letter. You have lost nothing. The friendship was only what it was while you were neighbors. You didn’t do anything to beat yourself up over. But, I wouldn’t pursue her farther.