Afaik you are not allowed to travel from dublin on an aircoach bus to drogheda. nor are you allowed to travel from drogheda to dublin airport. you can travel from anywhere in the south to anywhere in the north and vice versa. but of course you could say you were feeling unwell and ......
however a far better solution is to use the cie 100x route from dublin airport to dundalk via drogheda. the 100 route also passes the airport but stops everywhere while the 100x uses the motorway. stops at donore road in drogheda and at the bus office. if you are travelling from the city centre you would be far better using matthews coaches from parnell street. way way better class of coach and uses the motorway. stops in drogheda at donore road and just off the main street. afaik the 100 service is around 20 mins past the hour and the 100x at half past. from early till late.