There's no approval mechanism similar to the booking approval mechanism. However assuming that what you want to do is to stop people deleting past bookings to avoid being billed or deleting bookings at short notice, then what you can do is set the min_book_ahead. If you set it to zero it means that you cannot make, edit or delete bookings in the past. If you set it to say 1 day, then it means that you cannot make, edit or delete a booking at less than a day's notice.

Would that solve the problem?

Campbell