Quick answer
For JB Sentral without a car, use a cross-border bus via Woodlands or the KTM Shuttle Tebrau from Woodlands Train Checkpoint. Causeway Link lists CW1 from Kranji, CW2 from Queen Street and CW5 from Newton; SBS Transit 170X links Kranji and JB Sentral. Verify the current service and fare with the operator before leaving.
Bus from Singapore
Choose your Singapore departure point first. CW1 uses Kranji, CW2 uses Queen Street and CW5 uses Newton. SBS Transit 170X is another Kranji option. At border control, follow the operator's instructions for getting off, clearing immigration and boarding the onward service. A listed route is not a guarantee of a particular departure time or seat.
KTM Shuttle Tebrau
The Shuttle Tebrau runs between Woodlands Train Checkpoint and JB Sentral. It requires a separate train booking and the relevant immigration process. Check KTM's booking site for the date, fare and available seats; a bus arrival estimate cannot tell you whether a train has seats.
Driving instead
JB Sentral is in central Johor Bahru, so Woodlands is usually the more direct checkpoint choice for this destination. Compare the latest Woodlands camera images before committing to the drive. Factor in parking, Malaysia VEP status, Road Charge and tolls separately from the checkpoint queue.