You just reminded me of the time I caught the Dublin-Leeds Eurolines service that both under Bus Eireann and National Express sell tickets on. At Dublin bus station a not-that-modern Bus Eireann bus turned up for the service which was loaded on to the ferry. At Holyhead we had to alight the Bus Eireann coach and board a more modern Eurolines branded coach and the same driver took the different coach. It all seemed a bit strange.
That is not unusual for that service, one thing you may not have noticed was the driver was not the same one who put the coach on the ferry. A Bus Eireann driver and coach (usually a Eurolines liveried Scania PB) goes on the ferry where the driver makes a sharp exit off the ferry before it departs.
A second driver who works for a UK based contractor boards the ferry as soon as it has docked to take the coach off and drive it to the terminal where passengers are sent through Immigration/customs with their luggage and loaded onto a coach belonging to the contractor.
The passengers from Leeds are then loaded on the Irish coach which then is put back on the ferry and taken off in Dublin in the same way.
It can be the case that the coach only just makes the ferry, they will generally wait until the last minute for the Eurolines services but it has happened that one of our drivers has not made it off before the ferry departed.
I am not sure how this operation has come about, in the past a number of different methods were used including "shipside" where the coach leaves the passengers at the terminal to board as foot passengers and another is waiting at the other terminal.
The Dublin-London service is a through coach with a single driver, either one of our own Eurolines branded Scanias or an Irish sub-contractor and driver.
I am not sure what the situation is these days but it had always been the case that Immigration/Customs/Security in Holyhead insisted on the passengers and luggage being offloaded and made walk through the terminal checks even when on a through coach so the added disruption of a change of coach was minimal.
It is certainly a lot of faffing about in the early hours and hardly an enticement to use the service, mind you it still beats the five hour wait in Holyhead rail passengers have to endure.