There is both train or bus. If you take the train it is much cheaper to take a bus to Johor Bahru in Malaysia {just across the boarder) and catch the train there. There is both a day or overnight train. Have never used the bus but it would be cheaper than train I think.

I did Singapore to Melaka by bus. Big, comfortable bus with very few passengers. We did have to carry our luggage through customs entering Malaysia. Should be the same for K.L.

Simply google "bus service" or "luxury bus service" singapore to kuala lumpur" and you will find the names of some bus companies driving that route. The buses are very nice (reclining seats, a meal (not particularly good), fast and direct). You will also meet some interesting passengers. The ride is about 5 hours or so and, unless you are pressed for time, beats any of the alternatives. Also, the cost is reasonable.

you can try this two bus company

https://www.aeroline.com.sg/

http://www.transtar.com.sg/olcoachquery.php


aerolline drops you off at a hotel so i find it rather comforting and as for Transtar, get the one that drops you off at pasar rakyat. the one that goes to the main terminal at puduraya is very congested and sometimes, one have to be very careful..

Thank you all very much. This was very helpful!