How do I get from Guangzhou Airport to my Shenzhen hotel by public transport...bus or train?

From Baiyun airport, there is direct shuttle bus to reach Bagualing, Shenzhen. Upon reaching there, you can take taxi to reach anywhere you want to go. The bus journey cost around three hours.
Or you can take the local subway line 3 to reach GZ East Railway Station, where you can take bullet train for Shenzhen. The train journey costs around an hour and a half.

THANK YOU BETTY. I AM ACTUALLY NOW GOING FROM ZTK HOTEL SHENZHEN TO GUANGZHOU AIRPORT TO CATCH A 21.30PM FLIGHT. HOW DO YOU SIGGEST THE 2 OF US GO, WE WILL HAVE 2 LARGE SUITCASES EACH (4 CASES) AND 2 CABIN BAG LUGGAGE? tHANK YOU.

As I know, your hotel is only about 2km from Shenzhen Railway Station. Why not take the bullet train between Shenzhen and GZ? It is very convenient. You will arrive at GZ East Railway Station. Upon your getting off, you can go to the nearby Tianhe Terminal of Guangzhou Airport (CITIC Plaza) to take airport shuttle bus line 6 to Baiyun Airport.

THANK YOU FOR THE INFORMATION. IT IS VERY HELPFUL.