When you add Self-Book to your calendar or events, they can appear as signup links (for Group Signup and Appointment templates) or they can appear as buttons on the top of your calendar (Suggest an Event and Make a Reservation templates). See the image below:
By default anyone with who you have shared your calendar will be able to see the Self-Book buttons and signup links. However, if you don't want all of the visitors to your calendar to be able to see the Self-Book links and buttons you can change your Self-Book settings so that only visitors with edit rights can see them.
When you hide your Self-Book links and buttons, this will prevent anyone who doesn't have edit rights from booking events on your calendar. To hide Self-Book links and buttons follow the steps in the image below: