Secure Invites is a WordPress plugin that allows you to only allow invited people to sign up.
To scratch my own itch when developing Wibsite.com. Hopefully this plugin helps other developers too.
Yes, several users have reported it works fine. You just need to change the URL of the signup form from the default (wp-signup.php) to the BuddyPress page so the plugin knows which URL to secure. In addition, you can now automatically show the invitation form in your BuddyPress theme (if it is a child of the 1.2 or greater default theme, or it has all the same template hooks). Just tick the right boxes in the admin settings screen for where you want the invitation form to appear in your theme.
An invitation form can be easily put into your template page, look at the Installation details for more information.