There are good and cheap bus connections between KL and Singapore, mostly meant for business travellers. But don't worry...the busses aren't full of suits and ties. People travel relaxed. I used the AeroLine service from KL to Singapore for just 80 MYR in about 5-6 hours and can warmly recommend it. It is a through connection in a first class coach with leather seats and friendly service with just one toilet stop inbetween at a highway station. It runs along top-class smooth highways as quick as possible.
Visit their Malaysian web site where you will need to register (as said: meant for business people who will return time and again) but then can book and even select your seat online. You are provided with your PIN. You don't really need to print out the page as recommended, but you need to write down your PIN as you need it for check-in.
Half an hour before departure you have to show up at the Corus Hotel (a bit east of the Twin Towers) where you are provided with your ticket.
Border Crossing is also along the highway. Leaving Malaysia is an extremely quick operation (just need your passport). Entering Singapore after crossing a bridge with first great vistas, takes a bit more time, but is in very modern surroundings. You will need to bring all your luggage, which is scanned electronically; usually no need to open it. In case things are busy: After customs there is a display stating which bus to find in which bay. All extremely well organized!
The bus finally drops you off right at the Harbour Front Center. That is not exactly down-town, but just enter the center to find money exchange, restaurants, a huge mall, and especially the subway, which can bring you anywhere.
Find my own report here.
Certainly, this trip also works the other way round easily. Visit their Singapore web site for booking Singapore -> KL.
AeroLine also seems to offer rides from other cities in Malaysia. Visit their web site for details.