How can I go from Baiyun International Airport to Hongdu Hotel Zhuhai?

Well, the bullet trian is truely the fast way. However I advise you to take the airport long distance shuttle bus.
You hotel is very close to Gongbei Port, where you can take the Baiyun Airport shuttle bus to reach directly. You can take the long distance bus direct to reach Gongbei and then take a taxi to reach your hotel, which is faster than taking the bullet trains.
If you do not want to take the bus, you have to take the subway to reach South Railway Station from Baiyuna airport and then take the trains for Zhuhai. After that, you still have a long distance to reach your hotel.