For research purpose, I decided to take the express bus to Singapore one morning. I left home at 6.45 to go to the Gelang Patah terminal (which is less than 10 minutes drive from East Ledang). The bus departed at 6.55, arrived at Johor 2nd Link custom in around 15 minutes time. Since it was early in the morning, there was not much queue at the immigration checkpoints, so I was able to clear immigration pretty quickly. However, you do need to get off the bus at each checkpoint (Johor & Singapore). You'll find that people rush a lot to ensure that they will get a seat in the bus. I was too slow and too lazy to run around, so I ended having to stand throughout most of my bus trip. I arrived at the Jurong East bus interchange terminal at around 7.40. The bus trip costs RM4.
Overall, it was not a very bad trip and it's great to have alternatives transport in case if I am not able to drive to work in Singapore.
The buses do operate on very regular time intervals. You can find more details about the bus schedule here.
Bus interchange @ Jurong East (Singapore):