After all, one of Elizabeth's three cost-cutting measures was not to bring a gift back to Anne (a souvenir from London, perhaps?)! However, I also agree with others that Anne did get out a bit around her own neighborhood--she had to, to know Charles Musgrove well enough that he would offer for her--and decided that she never met Captain Wentworth's equal. So it is partly not being seen enough, and partly not wanting to be seen so much.