The last way that Wilbur ever communicates with Charlotte is by giving her a wink.  He does this as he is begin put into his crate to go back home from the fair.

He cannot say anything to her because his mouth is fulll.  But it is not full of food -- it is full of Charlotte's egg case.

To me, that is the real way that Wilbur is saying good-bye.  He is talking her egg case back to the farm so that her babies can be "born" there and he can have something to remember her by.