I suggest you take the subway from Guangzhou South Railway Station to Baiyun Airport and get out at the subway station along the way.
1) If you don&;t detour, take Line 2, get off at Haizhu Square, have a night tea at Yindeng Restaurant, or get off at gongyuanqian station, visit Beijing Road and have a snack, then continue to take Line 2 and turn to the north extension of Line 3 to go to the airport.