From Singapore, other than taking the conventiaonal route via the JB causeway towards Kukup (Pontian), there is another route if you are taking public transportation, that is going through Second Link (Linkedua), Tuas.
以马新第二通道的公交简略描述如下:Summary of the public transportation route (via secondlink) as below:
裕廊东地铁站Jurong East MRT-> 新加坡海关 Singapore Custom 〉马来西亚海关Malaysia Custom〉振林山 Gelang Patah> 笨珍 Pontian > 龟咯 Kukup