As far as I can gather (and this may be of no relevance to the OP's intentions - but to explore further some of the edge-cases mentioned by others) it's
a) determined to some extent by the administering local authority (i.e. they may interpret their obligations differently) and
b) determined by where you BOARD (but not alight) the bus.
Thus there have been reported and/or confirmed cases where
- (eg Red Arrow Nottingham <> Derby) one local authority deems this an express and thereby outwith the scheme, and the other does not. If you board within the Nottingham area you pay. If you board within the Derby area, you don't.
- (eg York Park & Ride) An otherwise normal stage carriage service exists to serve a P&R site. If you board at the P&R site, you pay. If you board elsewhere en route (even a nearby roadside stop) you don't. And when you board for your return trip, you don't pay.