Procedure as described by Pumikin is correct. MH times shuttle for all departing and arriving flight from JB. There is no real coordination with Changi flights since their goal is to assist Singapore residents use the much cheaper internal flights from JB. Anyone can use the service, you just gotta show up at the Orchid (which, BTW, is not located near anything). Coming back, there is a counter at JB for booking the bus.

You will have to carry your luggage through both Singapore and Malaysian customs at the border. No porters or carts, so pack light.