Exactly where in JB?

I was there yesterday, on Good Friday and probably it was a stupid thing to do because on Malaysian border I was stuck 2 hours waiting in the line.

If you just need to go right across causeway in City Square, it is quite easy thing to do: from Changi, go to MRT. From East-West Line (green) change on North-South (red) line and get out on Marsiling MRT. Get out there, cross over street, take bus #950. You will get out on both checkpoints - on Singapore and MY side. One on MY side - it is up to you what to do.

It will take 2 hours (minimum) from Changi to MY side. So if you plan to use public transportation, you need to reserve at least 4 hours minimum. However you can cut this time by half if you take taxi from Changi to the Woodlands Checkpoint and back. It will cost you appx $60 taxi fare both ways.