In Canada, we don't have "booking out" It's none of anyone's business when and where you fly, unless you are requesting access to controlled airspace. If you are required to file a flight plan, or flight notification, you are responsible for closing it too. But this rarely has anything to do with an airport, or operator, unless you chose them as your "responsible person".
The nearest I know of is "Booking it", which can either mean "but the ticket [for a commercial flight]" or, run or drive very quickly [to escape], seemingly a teenager term, 'cause I guess they need to escape every now and then...