Buses are often assigned to a route and then leave that route unexpectedly in the middle of the day to service another route (accident, other bus broke down, traffic, subway shutdown etc) , often not starting at the beginning of that route.

Then the bus changes its route number - certainly in the UK I see the drivers punching in the route details when they take over a bus.

Oh right, that makes more sense. I guess you could just keep a record of all the different routes in every bus though? And skip to the right spot manually as needed.