Best is if you can get a lane dedicated entirely to buses, and ticket cars that drive in it. You want buses to be a pleasant alternative to driving -- since you already have a walk at the beginning and end of your journey which takes time, it's nice if your bus can get priority over car traffic.
And from there, build up the areas with good bus service more and more, add more buses as needed due to population growth, lengthen lines, add new lines gradually as people see the success of the first ones. Incremental implementation is the trick.
Counterintuitively this even is useful for people who have to go by car. A bus has a lot higher density in people transported. By making it attractive for people to use the bus they don't take away space on the road, which can increase the flow of the remaining cars, even if road space is reduced.
For people to use the system, they have to trust the system. Depending on the city, rail infrastructure can get you close enough to walk to many places. The stuff that crushes trust even then is the rail lines being off schedule and strikes. Safety can be a major concern too, like the woman who was raped on a SEPTA train recently (WTF). These should be simple asks. Maybe we just need to charge/tax more so they have more money (or maybe we need better people making the decisions with that money).
Separately, there's a chicken-and-egg problem. In order to run busses every five minutes—which is what you really want—you need enough bus riders to fill all those vehicles.