Bus Eireann provides buses from Bus Aras in Dublin City Centre to Tralee (Route 285) and Killarney(Route 284), where there is a connecting Bus Eireann bus to Dingle.
See www.buseireann.ie for journey times from Tralee and Killarney to Dingle.
There’s a coach service from Dublin to Tralee, that has regular runs, and reasonable fares. Onward taxi and bus links can be arranged from Tralee to Dingle.
The train route is Heuston Station, Dublin to Cork and to the Tralee line. Duration: Approx: 4 hours.