The booking approval process is very similar to the The User Approval Process and is a matter of changing a booking's status from Requested or Tentative to Approved if the booking is to be allowed, or else to Denied. The only major differences are that:

Bookings may be created pre-approved so that no one needs to manually approve any bookings, or perhaps only some bookings.

Delete a booking request if required, provided Permissions have been suitably configured, however doing so would mean the removal of the booking attempt from reports that might be created require.

To approve bookings, go to the The Booking Requests Page  which shows all the booking requests and provides easy ways of approving them. It also offers a way to edit the bookings, if required.