Make sure you get a Luas / route 90 add-on. You should be able to get a through ticket, but I'm not sure if it would be any cheaper.
Alternatively walk from Heuston to Blackhall Place (James Joyce Bridge*) and get a Dublin Bus route 37, 39/a/b (most frequent), 70/a towards Blanchardstown. 37x doesn't stop in Ashtown.
www.mkmap.com/dublin
http://www.dublinbus.ie/en/Your-Jour...-Timetables/37
http://www.dublinbus.ie/en/Your-Jour...metables/39ac/
*
http://www.google.ie/#hl=en&source=h...6f6d0aa5aef338