The most convenient way to travel between Zhongshan中山 and Hong Kong airport is by ferry. (For information on how to travel between the airport and other places in Guangdong, read here).
The ferry operates four or five times daily in each direction. The timetable is shown below. Note that one of the rules for travel is that your ticket is for the same day departure – it’s not clear whether you could take the 6.30 ferry for a departure after midnight, for example.
The ferry travels between the “Skyport” at Hong Kong airport and Zhongshan ferry port, which means that you can skip passport control and baggage collection at Hong Kong airport, instead doing it at Zhongshan port (which is part of mainland China).
You may also be able to skip baggage checkin at Hong Kong, depending on which airline you are flying. At Zhongshan ferry terminal there is a check in facility similar to the one at the Airport Express. To use it, you need to check in at least three hours and ten minutes before your flight is scheduled to depart, and your airline needs to be one of the participating airlines – you can check the list on the ferry website but that seems not to be the case currently, so maybe best to check with the ferry company by phone. If your airline is not participating you can take your baggage onboard and check them in at Hong Kong airport. This will be in the “Skyport” area which sits airside from passport control, so you won’t need to enter Hong Kong to do so.
Tickets are pricy at about 290 RMB one way even in standard class from Zhongshan, or $260 one way from the airport – current prices in HK$ are here. You can book on the website as well as in person at the ferry counter in the airport and ferry terminal in Zhongshan. You may be able to find cheaper tickets with a travel agent if you can be bothered to look around.
The ferry terminal in Zhongshan is located some distance from the city centre, although the ferry company operates a shuttle bus service timed to coincide with ferries. A map of the port location is below.