The last time we went from Singapore to Malaysia we went by taxi. It was straightforward and easy. At the border we gave our passports to the driver who showed them to the guards and did all the talking for us. He dropped us at the train station in Johor Bahru and we began our Malaysian journey from there.
This time we went by bus. There are lots of companies you can book on line. We used the website https://www.busonlineticket.com We looked at all the reviews and decided to go with Luxury Coaches who seemed to have the best reviews. We had to check in at the office at 7:30am with a departure time of 8am. Everyone was on board and we left 10 minutes early. We were each given a bottle of water. After a brief stop at both sides of the border where we had our passports scanned at the Singapore side and we had to remove our luggage to be scanned at the Malaysian side. We also had a brief 20 minute coffee stop. All in all the journey took around 5 hours. We were now in the UNESCO World Heritage city of Malacca!