Is there a logic to the numbering of bus routes in the London area, such a
1-100 means one thing, 101-200 means something else, or are they random,
maybe loosely based upon a logical system of long ago that has fallen into
disuse?

I defer to those who know what they are talking about but I think there were
at least some basic rules. For example 1-99 were routes that orginated in
central London, 2xx were once single deckers, 3xx were London Country routes
north of the river, 4xx London Country south of the river and so on.