1) Requirements. This functionality available in the Booking Calendar update 8.0 or newer version.
So if you are using some older paid version of Booking Calendar, then you can request the new update of Booking Calendar on this page: http://wpbookingcalendar.com/request-update/
2) Requirements. Additionally for ability to export bookings into external websites, like Airbnb, Booking.com, HomeAway, TripAdvisor, VRBO, FlipKey and any other calendar that uses .ics format, you will be need to install Booking Manager plugin update 2.0 or newer ( https://wordpress.org/plugins/booking-manager/ ).
3) Export URLs. Now, when you have installed both plugins, you can start configuring of export bookings into external website.
Please open the Booking > Settings > Sync > Export -ics page.
Configure URLs for each booking resources (in paid versions). In the Booking Calendar Free version, you will see field for configuring URL for your one Default booking resource. Then click on Save changes button.
4) Import .ics in external website. Now you need to check documentation of each other external website, of how to start import of .ics feeds into specific services: Airbnb, Booking.com, HomeAway, TripAdvisor, VRBO, FlipKey
Important! Please note, once you have imported specific .ics feed into external website or application, its does not mean that this operation will be executed periodically. You need to check documentation of specific service (like AirBNB), for ability to import such .ics feeds periodically for having your bookings in external website always up to date.
Example of how to import .ics files in Google Calendar.
Tip. In case, if you start import of .ics feed into Google Calendar by URL "Other Calendars > Add by URL", then in the point #3 you need to configure URL that ending with wpbm.ics. For example: