I am not clear which pre-published timetables you are referring to, the ones in the zip file (which are complete timetables) or the stop-specific timetables (as for 11 and 23 in Brian’s post) which only give approximate frequencies for high frequency periods of operation and are best thought of as summaries. Nor whether the ones you get from the API are complete or summary.
The “high frequency” point is important as TfL monitoring of those is basically of the service intervals, not whether a bus is where it should be. In theory every bus on a route could be 20 minutes late but the service intervals (and thus the service as perceived by passengers) could be fine. Such a situation might indicate a substantial delay but the delay may have happened two hours previously and subsequently cleared.
While they are related to some extent, I am interested in whether my bus is going to arrive at my stop
when it is supposed to but also in whether I am likely to be delayed once on the bus. In some ways the latter is more important as I have a range of apps which tell me when the bus is coming with pretty good reliability. In an ideal world a screen on the bus would mimic what motorway signs do and cycle though information like “North Finchley in 15 minutes”, all based on current traffic conditions. Well, I can dream…
Low frequency (less than every 12 minutes) services are monitored in the traditional way, against where the bus should be according to the timetable.
While they are probably not useful to you, as they are not directly reusable electronically and only show major timing points, there are other sources of timetables in matrix form. TfL publish every single one of their bus working timetables in pdf form - see Bus schedules - Transport for London. There is also the London Bus Routes site which contains html and pdf timetables. They come closest to the timetables TfL used to post at stops before they decided that the London public was only capable of digesting times at one stop - see London Bus Routes.