The immigration clearance process for your Malaysia and Singapore journey is pretty straightforward. You can take the below checklist into consideration -

Before reaching the land border, the buses stop at the checkpoints for Malaysian immigration clearance where you will need to present your passport and any necessary visas. Make sure you have a valid passport.
After crossing the border into Singapore, there is another process for Singaporean immigration clearance. You will need to disembark the bus with your luggage and proceed through customs and immigration.
In Singapore, you might be required to fill and submit a disembarkation/embarkation card. Your fingerprints and photograph will be captured as per official process. Keep the disembarkation card with you as you will need it when you leave Singapore.
Once you have cleared Singaporean immigration, you can re-board the bus and continue with your journey.

The entire immigration process usually takes between 30 minutes to an hour, depending on the amount of traffic at the border checkpoints and the land borders. This traffic at the checkpoints is usually very high during peak times like Chinese New Year, School Holiday weekends and other festive ocassions with wait times of around 2-3 hours or more.

It's important to note that the immigration clearance process may differ slightly depending on the bus operator and the specific border crossing used. However, by being prepared with the necessary documents and allowing enough time for the process, you can ensure a smooth and hassle-free journey between Malaysia and Singapore.

Kuala Lumpur to Singapore Bus Tickets