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.