I will go from Huaxia Hotel, Guangzhou to zhuhai, so whether there is a bus leaving from the hotel

I'm afraid not. For certainty, you'd better go to Guangzhou Provincial Bus Station (near the Railway Station) to take a direct long-distance bus to reach the other city which operate from 06:30 to 21:00 every 20-30 min.
from your hotel to the bus station, you can take a taxi there. It may take about 10-15 min.