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
Jurong East MRT bus interchange 裕廊东地铁站巴士转换站
注1：从新加坡关卡至马来西亚关卡，只要是causeway link 公司的巴士都可以上车，
P/S1: You can board any Causeway Link buses from Singapore Custom heading towards Malaysia Custom, be it the same bus you took from Jurong East MRT or originated from Boon Lay MRT, as all will still to alight at Malaysian Custom for clearance.
得注意一定得乘搭往Gelang Patah 振林山为终点的巴士 CW4 ，巴士停靠的位置通常是便利商店外，有时却在马路外， 上车前一定要问司机或在在那里执勤的causeway link员工：“Gelang Patah?"
P/S 2: Do take note to board on the CW4 Causeway Link bound for Gelang Patah , which normally parked at the first bus bay in front of the convenience shop. It's always a good idea to ask double check with the bus driver or the Causeway Link worker ("Gelang Patah") before boarding on the bus. Sometime bus parked outside the shelter, due to other buses occupancy of the lane.
Interior of Causeway Link Bus (@Gelang Patah) 巴士内观 (摄于振林山）
注3：振林山往笨珍的causeway link 巴士号码为52T，车费为马币4.20,
这不是一条巴士频密的路线，以同一辆巴士不断来回振林山与笨珍， 所以如果错过了得等上2或3小时（周末通常每2小时一趟， 除了午餐时间），详情可以参考causewaylink 的网页.
P/S 3: Take the Causeway Link bus 52T from Gelang Patah to Pontian. Due to the fact that this route is not a popular route, thus there is only a bus arranged to back and flo Gelang Patah and Pontian. So you will have to wait for 2 or 3 hours if you miss the bus (For weekend, will be 2 hours for the next trip except lunch hour-3 hours). For detail bus time table, please visit their website for details.
要省钱还是省时间。省钱就乘德士往凤梨镇 Pekan Nanas后（吩咐司机停在大众银行Public bank那里的巴士站），转任何往笨珍的巴士（ 一般是从larkin 开来的Maju 96巴士，费用是2 马币）。省时间就乘德士直往笨珍好了。(德士收费：往凤梨镇 RM25, 往笨珍 RM40-50; 司机不使用计表，小心被砍菜头)
P/S 4: If you do miss the 52T bus, the only option for you is the taxi. But you do have 2 options in taxi - budget or the convenient way. For budget mode, take taxi to Pekan Nanas, and board any bus towards Pontian (Normally it's Maju 96 bus from Larkin, RM2 from Pekan Nanas to Pontian); For convenience, take the taxi straight to Pontian or Kukup ! Taxi fare from Gelang Patah to Pekan Nanas RM 25, while going Pontian cost RM40 to 50, drivers will not use the meter, so beware being quoted high)
Even though going to Kukup via the second link (Gelang Patah) is more complexed and you will be troubled have to prepare the small change in Ringgit (bus driver does not give the change) . But my personal opinion is commute via secondlink tends to save the time and traffic smoother provided you able to catch the 52T bus (exceptional during long weekend or school holiday)