...I remember once in Zurich when my local bus was two minutes late. The people at the bus stop were really quite cross.
There's enough slack in the timetable to account for delays. If the bus would normally take one minute to get from one stop to the next, the timetable will actually account 90 seconds, etc.
Then there are certain stops where the bus will, if it gets there early, stop and wait. They don't do this on every stop, but they're frequent enough to keep the service regulated. Intelligently, these stops are also the ones which synchronise with other transport systems. For example, when I take the train home from work I know that there'll be a bus waiting for me when I get off at my station.
It's not perfect, but the overwhelming majority of the time it Just Works.