Ciao Valentina!
I'm glad that you're planning to visit Doolin. To find out the best way to travel from Dublin to Doolin, I'd like to recommend checking this useful
journey planner: as you can see, there's no direct bus from Dublin to Doolin, so my suggestion is to take the bus from Dublin to Galway. Then, once you get there, you'll be able to take another bus that will bring you to Doolin.
Please, let me know if you have further questions regarding your trip. If you prefer, talk to me in Italian!
:)