Thanks @LeonByford
In the hope that it might offer some clues as to what is (presumably) going wrong between TfL and BODS, let’s take a specific example. If I ask bustimes.org to map the 15, I get a mixture of weird and wonderful misreports. SE66 is currently somewhere round Abbey Wood on the 244, according to LVF, but on the bustimes map it is labelled as 15 to Charing Cross. If I click on it and look at the history I see
I’m not sure what “history” means when some of the times are two hours in the future but look at the pattern: 15-15-483-15-15-483. Wrong operator and destination (for the 483), wrong number of decks (for either).
Theories on a postcard…