I only want Members to be able to book for a specific event. How do I set this up?

There is a checkbox labelled ‘Logged in members only’ on the event setup page when creating or editing an Event.

By ticking this box, the booker to the event will have to log in to make a booking, there will be no public bookings available. 

The "find me" that asks for the bookers name and email will not get displayed if this option is checked.