Hi, there is no direct shuttle bus from HKIA to Royal Plaza Hotel, you can take Airport Express to Kowloon Station and then take free shuttle bus K5 to yout hotel. The fare would be HKD90 per person and it takes around 35 munites including the train ride and the bus.
You can also take Bus E32 to Cheung On Bus Terminus and there change to Bus 44 and alight at MONG KOK EAST RAILWAY STATION. Costs around HKD20 per person.