Is there a immigration stop or is it something I would need to do before jumping on the bus at Singapore?
The bus would be by 12go.Asia:
Golden Mile Tower - Berjaya Time Square, KL
When travelling by bus from Singapore to Kuala Lumpur..
The bus crosses the border where you get off the bus with your belongings to cross through immigration and security and the bus waits for you on the other side. It was easy and quick.
I did this exact trip less than a month ago with 12go but reversed, one stop for exit stamp from Malaysia about 15 mins and a second stop for entry to singapore bout 20 minutes. The only problem was people who hadn't filled out necessary forms for arrival to singapore were held back and consequently the bus left without them after waiting 40 minutes total so just be prepared!