Extension You Have a New (BuddyPress) Message

This plugin is as simple as it is useful. Add the widget or use the shortcode [you-have-a-new-message] anywhere to display a notice if the currently logged in user has new messages. The notice links to the user’s inbox as a convenient and omnipresent shortcut.

Message texts can be configured via widget interface and shortcode parameters, e.g. [you-have-a-new-message single="new message" multiple="%s new messages"].