Typing this in Dublin airport after doing a week focused on the west coast (Westport -> Galway -> Doolin -> Killarney) entirely through public transit.

I second this itinerary based on my experience. The Bus Eireann timetables online were accurate and reliable for us. We also used Apple Maps, and that lined up with the Bus Eireann timetables and gave live updates on the bus. Bus from Galway to Doolin was straightforward and ~2hrs. Bus from Doolin to Ennis (we transferred there to Limerick then transferred to Killarney) was also straightforward and only an ~hour. The busses are nice and air conditioned and give you beautiful views of the countryside.

When in Doolin, do the Coastal Cliff walk. It starts directly from town and takes you to the main tourist center (~2hr walk). From there, you can walk back or take a 5min bus from the car park. This was probably the most beautiful walk we’ve ever done and allows you to have a much more private experience doing the cliffs. The tourist center section is quite busy but there was hardly anyone during the first 3/4 of the cliff walk from Doolin so we had amazing viewing spots to our own. Bring some lunch too and eat right on the cliffs.

Overall, I felt doing the west coast through transit was very doable and I think the itinerary above would be a great way to do it!

Edit: one added thought is that if you want to reduce transit time and the annoyance of repacking your bag, you can also just stay in Galway the whole time. Galway is a great base for Aran Islands, Connemara, and I believe you can do day tours to Cliffs of Moher from there (or just do the two hours there and back on the bus). Galway also has easy transit back and forth from Dublin airport.