Does someone have details and the route of the free bus service from/to Hong Kong (HKG) airport to the city ?
There isn't a free public shuttle bus service to/from the airport. (There are, of course, normal paid public buses that serve HKIA.) What I think your relative may have gotten it confused with is complimentary hotel bus services that are reserved for guests.
I'd recommend taking the HKIA Express though. It's a lot cheaper ($100) than getting a taxi and a lot faster than a bus given Hong Kong's traffic, and if you're going to the airport many airlines now offer check-in desks in the city itself, before you get to the airport.
Once you have paid for your ticket and caught the HKIA express:
Free shuttle bus service is available, taking passengers from Kowloon or Hong Kong stations to most major hotels and transport interchanges. Passengers can also enjoy free porter service at all Airport Express stations.
So if you have a hotel near Kowloon or Hong Kong station, you should be able to get a free shuttle bus once you have taken the Airport Express.