Is there a shuttle bus from Guangzhou Airport to China Hotel 122 Liu Hua Lu, Yeuxiu District ?

No direct shuttle bus can take you from the airport to your hotel. You can take the airport express line 1 to reach its terminal near the local railway station and then change a taxi to reach your hotel.
Or you can take the local subway line 3 to reach Jiahewanggang Station where you can change to line 2 to reach Yuexiu Park Station. Get out of the station from D1, you can easily find your hotel.

Hi Dave - thank you very much. So maybe its easier to just take a cab?

It is easy to take a cab directly, but the fare may be high. It is around 100RMB.