Yes, you can definitely require your approval for all bookings.
This feature allows you to approve each appointment before it is finalized.
Click on the Settings tab on the left side menu bar.
Under Your Settings, click on the Booking Settings option. This will now show your booking settings options on the right side of the screen.
To require your approval before bookings are finalized just check the box next to the text "Require your approval before online bookings are finalized". Hit Save.
To change this feature back if you do not require approval before bookings, simply uncheck the box and hit save.