One way to do this in a more natural way would be to quietly make the city's environment more hostile to cars and driving. This could include things like physically less parking spots (they would have to be replaced by parking outside the city though for a place like Perth); thinner roads including the major thoroughfares; more speed arrester installations like roundabouts, speedhump, those diagonal curb things.
One thing i wouldn't do is overtly privilege another mode of transport above the others. It seems to set up a zero sum competitive positioning in drivers minds. Ie, the bike get a lane, and I lose a lane, etc.