It looks like different permissions are needed for each of these. For the RetrieveBooking you need to have APPOINTMENTS_READ if you’re using OAuth. If you’re not using OAuth, or you think you do have this permission please provide your application id as well as the merchant/location id in question.
I’ve tried both Square API Explorer and OAuth with scope of scope=MERCHANT_PROFILE_READ+APPOINTMENTS_READ+APPOINTMENTS_BUSINESS_SETTINGS_READ
Application ID = sq0idp-K6eDLOzN4XnwejEuVEhT7w
booking_id = sxp9vr7u4krewo
It looks like that booking was created outside of the API. At this time, the Bookings API currently only has the ability to read appointments created directly by the API.