I was on the bus the other day leaving Oxford and I saw exactly that happen to someone trying to get on my bus. The driver could easily have let the guy on the bus, so I emailed the bus company to query their procedure.
This is what I was told:
Prior to departing a stop the driver is to:
1) look in their mirrors to ensure there are no persons intending to board their vehicle
2) Close the doors
3) Put on indicators to show that they wish to move out right
3) Look constantly in both offside/nearside/inside mirrors to look for any obstacles and ensure that persons are safely seated
4) If safe to do so move off from the stop at slow speed
Once the driver has closed their doors and started their checks we state they have commenced their manoeuvre and should therefore not pick up again on health and safety grounds.
As you can imagine the issue surrounds point 1. If the driver did not see the person in time they will commence their manoeuvre, however the intending passenger may believe they should have been easily seen creates conflict over the interpretation of the incident.
Additionally, if the driver was due to depart a few minutes earlier they will at some point have to commit to making progress and departing, as they have a responsibility to operate the service on time for the other intending passengers left waiting at stops further up the route.
Can't really argue with that. They have to pull away at some time and they are only following procedure. In Oxford, where the buses are quite popular, you can be left sitting on a bus for ages waiting for it to pull away from the city centre while there is a steady drip of people constantly getting on the bus.
Don't get me started on the summer foreign language students!