He dreamed he was writing with the Countess, and travelling with her and talking to her; and he woke up with the determination that the thing should be done if it were possible.

Why not?
She often made a trip to her native country, as she herself had told him, and why should she not make another?
For aught he knew, she might be thinking of it even now.
Then he had a reaction of despondency.

He knew nothing of her ties or of her way of life.

A woman in her position probably made engagements long beforehand, and mapped out her year among her friends.

She would have promised a week here and a month there in visits all over Europe, and the idea that she would give up her plans and consent, at the instance of a two days' acquaintance, to go to America was preposterous.