Having read what Dylan has to say about himself, it is fairly clear that he doesn't want to be "His Bobness" and never thought of himself as "His", "Her", or "Your" Bobness.

I think using the phrase journalistically is way of talking about Dylan without actually saying anything about him.   

This is probably a shrewd trick on the part of journalists, who have a history of getting Dylan wrong, and want to avoid the whole "Something is happening here, and you don't know what it is, do you, Mr. Jones?" thing-