Exposure offers a variety of ways you can share your story a bit more privately.
You can:
Hide you story entirely, making it only accessible to those who know the URL
Hide your story from your feed (helpful if you want to use categories to keep your landing pages clean)
Add a password in case you don't trust the obscurity of the link.
All of these settings can be accessed while Editing a story, and clicking on "Options" in the header. The Story Options panel will appear on the right of your screen.