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:
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.