There is a bus - 76 I think from the West County in Chapelizod to Tallaght but you have to get a bus (25a that goes past Superquinn) to Chapelizod first and then another bus. It takes forever any time of day. The best option would be to drive, should take approx 1 hour. I know someone that works in the Square and lives at the Spa Hotel and it takes them 1hr 15 mins.
Sorry Help Me, I live in Lucan, but have never heard of a bus that goes that way, but I wasn't looking so I might have missed something. Are you travelling to work? Is there someone else you could share a car with? You might be surprised that a lot of people are happy enough to give lifts? (I work on the northside and do that one day a week, otherwise I would have to take a bus into town/back out).