For the first time ever, and with considerable disapproving suspicions  from JB locals, I caught the Transtar bus from Johor Bahru CIQ in  Malaysia to Changi Airport a couple of days ago.  
The bus cost MYR 10.00 and I used Uber to get to CIQ, a journey of  2.53km, for MYR 5.53.   So all up, it cost MYR 15.53 door to door.  
And it went ...   FINE!  
But I'd only do with with carry-on luggage.  Trolleys seem to be  non-existent and you do need to remove all luggage at the Singapore end.   There's also a fair bit of walking where escalators seem to be  preferred.  The bus has some limited on-board luggage storage however.  I  found the bus again without problem after going through the Singapore  procedures.   They even told me that, if by chance I get delayed and  miss the bus in Singapore, to get then next one in one hour ...   But no  need this time. 
   For me, and I know I was lucky, it was pretty quick across the  causeway - car or bus.  And it was minimal waiting for passport control  or customs at either end.