I think the key phrase to help you understand is a glimpse of Arabella. He is not stopping to chat with her- he just wants to see her as he goes by, but not so near or in such a way that she knows he is looking at her. To actually have an appointment to talk with her would have been, in those days, a rather complicated thing, with certain protocols and preliminaries, and he may not be ready yet to commit to all that.
It's been a long time since I read that novel, so my understanding may not be correct, but that's what I get from the few lines in your post. It seems plain that he would not be going to see his aunt were it not that his path will take him where he can see Arabella, but if anyone were to ask him why he was going that way, he had the handy excuse that he was going to see his aunt.