I traveled to Singapore from Malaysia by bus. What is quite convenient, because the flights to Malaysia – especially to Kuala Lumpur- are way much cheaper than anywhere to South East Asia.
You can take a bus, or a train, to Singapore from many different cities, but probably the easiest are to go from Kuala Lumpur (around 6 hours drive), Melaka (4 hours drive) or Johor Bahru, which is on the border with Singapore. I went from Melaka, and the bus journey took around 7 hours. It really depends what time of the day it is, since it is just crazy on the borders during the rush hours. So don't plan too much ahead and don't be surprised if the bus takes twice longer than what was advertised.