I found a person who wants a book that I have and I would just as soon send it to her without getting than have it on someone's wish list and go through several people--when I want to mail it, I want to do it QUICKLY!  How do I do this?

She should WL the book and you can post it directly to her WL.  Just go to her WL and hit "Post This Book".  If she puts it on auto-request you don't even have to wait for her to log back in and accept it - it'll show up as requested from you after the 1 hour buyer's remorse period.

For books already on your bookshelf, there is an option to "Send to a Friend"  which does not involve credits.  BUT you need to enter their whole address into that option.  It does not work for WL books.  But it is great to keep the book's footprint (history) when you are sending deals.

That sounds like a neat feature.  Does it show up on your transaction archive or count as a book you've mailed on your profile?

If it's a wish list book (check the ISBN) then do as Danyun suggested.  There's a help doc called "Can I post a book directly to someone's wish list" that will walk you through it.  If it is not a wish list book, you can post it to your shelf, and the other member can order it from your shelf.  There's a help doc called "How do I send one of my books to a friend?" that should help.  It will explain about mailing to a friend, too.  I don't know if mailing to a friend counts in the tally.  Interesting question.

It shows up in your transaction archive as a separate category.   Along with From you and To you.