That is very early for their buses, Clarke Quay is not that far away. Mind you we are in the Holland area and it used to take nearly 40 mins door to door from Dover (I drive mine now).
All school buses take a long time to pick up everyone since they go door to door, it sounds like you must be one of the first pick ups for that bus. How long did they say the bus would take? That is a long ride for a 4 year old. What about at night? What time are they expected home? Are they a first drop off at night? Normally that is the way it works if they can do it.
Public transport can be hard, the MRT will get you there, but the walk from the station to the school is quite a way, and it could take just as long causing you to leave at the same time. Not too sure about regular buses. You can check on the bus websites for routes etc and timetables. Here are the sites but can't guarantee you will find a way there.
Quite a few people use taxis as well, sometimes with a few kids it is not that expensive.
The other alternative is to go only one way on the bus, perhaps only do the homeward bound trip? Quite a few people do this.
Welcome to Singapore and I hope your boys enjoy Dover Court, mine do.