Taking a bus from Singapore to Johor Bahru is the most economical mode of transport. There are many bus services around Singapore that can bring you across the border. Even if you decide to go on a last minute day trip to Johor Bahru, you can still take a bus and reach in time for a few hours of shopping. Of course, there is also a high possibility that you might be caught in a traffic jam near the customs.
If you are looking for the shortest and most comfortable way to travel from Singapore to JB, you may want to take a train instead.