Are timetables still a thing? Here, for example, he bus stops show that during peak hours, the buses run every 10 minutes, off peak every 15 minutes.
For the most part, they exist but aren't a thing for many, I guess
with bus services, if it's a 'frequent' service (every 12 minutes or better in London, every 10 minutes or better outside London) then punctuality monitoring by TFL / Traffic Commissioners' staff is done on headway, rather than exact adherence by each bus to its scheduled times, on the understanding that if service is that frequent, most people will just go to the bus stop and wait rather than look at a timetable before going to the stop, and if every single bus is X minutes late, the passengers won't know or care, but if there's 3 buses together then a long gap, they will.
i'd be inclined to say a 15 minute headway should have the times (as in buses will be at X time then every 15 minutes until Y time then whatever)
and yes, there will be a timetable, vehicle working schedule and driver duty schedule, even if the service is every 2 minutes or less (some London routes are - or at least were before covid - that frequent) but it's more a basis for further negotiation, as the controller will often ask drivers to run a few minutes early or late to keep the service even.
there are ways and means of doing this - what happens too often in London is that everything ends up at the speed of the slowest bus / driver on the road, and buses get 'held at this stop to regulate the service' one or two stops before a major interchange where many passengers will want to get off.
anything that's not 'frequent' should have and run to a timetable.
You obviously live in a city! Buses go once an hour or every two hours here.
there are services that run one return journey a week, or the second tuesday of the month, and so on...