You can synchronise bookings via Accommodation Channels, or using an iCal feed.
For accommodation channels we use Smoobu, a service you subscribe to which will synchronise your bookings with other providers such as booking.com, expedia, Stayz, Airbnb. Smoobu charges you a fee.
Alternatively you can use a free iCal feed if the other provider supports it. Airbnb provides this (two-way).
To use an iCal sync, for each room which will appear on another service, edit the Room Details and enter the inbound iCal feed endpoints which you got from the other provider (e.g. Airbnb), and/or copy the outbound endpoint provided by the Booking Service and paste that into your administrator configurations in the other provider’s website (e.g. Airbnb).
iCal sync inbound is checked each time a booking is made that involves a room with an inbound sync. So you can’t get a double booking.
Outbound depends on the other service, e.g. Airbnb only checks every few hours, so you can’t use Instant Book on Airbnb.