Since I am going to be doing the same thing in a couple of months, I did some research, hope this helps:

<i> Buses leave for Johor Bahru from the Queen St. station on the corner of Queen and Arab Sts. Air-con express buses ($S2.40,1 hour) depart every 15 minutes, public SBS bus No.170 costs $S1.10. Buses stop at the Singapore checkpoint, keep your ticket and hop on the next bus as the bus wont wait for you while you clear immigration </i>