Hello,
Guangzhou South Railway Station is located in Panyu District, Guangzhou, and Baiyun Airport is located in Huadu District, Guangzhou.
The distance between the two districts is still quite far. If you take a taxi, you have to pay the bridge toll, which is about 180-200 yuan.
My personal advice is that it is cheaper to take the subway, which saves time and money, and the most important thing is that there will be no traffic jam.
But it is necessary to match your travel time.