We are not comfortable driving...how accessible will public transportation be to get us from Dublin to Killarney to Kilrush to Shannon Airport?

For Dublin-Killarney, the train (www.irishrail.ie) would be your fastest option. The bus (www.buseireann.ie) would be cheaper.

The bus is probably your only choice for your other routes. For Killarney-Kilrush, you probably would need to go via Limerick. According to my Lonely Planet Ireland guidebook, Bus Eireann has more frequent service between Limerick and Kilrush in the summer than it does in the off season. The same is true for local bus service from Limerick to Kilrush.

This is the second thread you have started without a sufficiently informative header.

The coach (bus) is the most economical transport and the best opportunity to actually meet other folks. You just have to be able and ready to work around the timetable.

There are BusEireann routes that use the ferry across the Shannon estuary from Tarbert (Co. Kerry) to Killimer (Co. Clare). There should be local bus service from Killimer to Kilrush and/or Kilkee. Unfortunately, in off season, local bus service may only be available in early morning & late afternoon.