Avoid peak hours.
Morning Jams will be around 6:30am to 9:00am (Singapore to JB) and 5:30am to 9:30am JB to Singapore.
evening Jams will be around 5:50pm to 10:00pm Singapore to JB. Not sure about JB to Singapore.
The day to avoid is Friday evening from Singapore to JB and Monday mornings from JB to singapore. Why? reason is because there are more traffic due to Malaysian who work and stays in Singapore but return to JB for the weekends.
The timing I give may not be accurate but roughly it about that from past experience. After the RM20, it may or maynot change.