I will be staying at Macau Royal Hotel and crossing over to Catic Hotel in Zhuhai. What is the roads i should take?

Take the free shuttle bus from your hotel to Sands Casino, where transfer to Sans' free shuttle bus to Gongbei border. Cross the immigration border and you will be in ZH Gongbei. Then you can walk to Overseas Chinese Hotel bus stop to take bus no. K3 or 2 to Jida Station,which is around 900m from Catic Hotel.

Thanks Byan, Instead of taking bus in ZH, is the cab expensive from ZH GongBei to Catic?

No, it is not expensive at all. It is 6-7km between Gongbei border to your hotel then, so the taxi fare will be only around CNY20.