Please advise best route for an afternoon departure in Dublin heading to Dingle, Tralee station. Thank you!
I'm not exactly sure what you are asking, but you can find bus schedules at: www.buseireann.ie. You won't be able to get any closer to Dingle by train than Tralee.
If you were to go by bus all the way from Dublin to Dingle, the last bus you could take leaves Dublin at 11:30. Change in Limerick and Tralee and arrive in Dingle at 19:10.
If you were to take the train from Dublin to Tralee (change in Mallow), leaving at 11:00 will get you to Tralee in time to catch the 16:15 bus which arrives in Dingle at 17:20. If you leave at 13:00, you will arrive in Tralee in time to catch the 18:00 bus which arrives at 19:10.
If you must wait until afternoon to leave Dublin, then your only choice is the 13:00 train.