Are there daily bus services from HK to Quanzhou? If so, how can I avail of the services?

There is no direct buses to reach QZ from HK, so you need to reach Shenzhen first.
Upon you reach Luohu District in Shenzhen, you can walk to reach Qiaoshe Bus Station where you can find some buses to reach QZ directly. The buses are at 21:20, 21:10, 21:00, 20:50, 11:40, 20:55, 21:40, 20:40, 21:30 and 10:40.