Hello Cathy,
That sounds like a lovely plan. For your situation, the use of buses and trains seems like the most suitable option. Some buses operating longer distances have onboard toilet facilities, but not all. All of Bus Eireann's new Expressway (
https://bit.ly/3LzPRrS) fleet, for example, have onboard toilet facilities. Many long distance buses take regular restroom breaks. This is a good general article about Bus travel in Ireland (
https://bit.ly/431KaKe).Another good option you could consider is using one bus tour operators, and it will be easy to confirm with them whether they will have the required facilities onboard. I can recommend looking Tourism Ireland's Tour Operator listing (
https://bit.ly/49VZf2r) with useful filters and links to each operators website. Just let me know if you need any recommendations for possible operators for a specific itinerary.
Rail travel in the Republic of Ireland is operated by Irish Rail (
https://bit.ly/3FrUUVG) and their trains have toilets. You can find more details of the services they provide in each category here (
https://www.irishrail.ie/en-ie/about-us/iarnrod-eireann-fleet/intercity-fleet). I chose the intercity category as an example and you can change this from the left side panel.
A good overall resource for planning your trip is Transport for Ireland's Journey Planner (
https://bit.ly/3T6hbR0) as it includes both buses and rail.
I hope you you find this useful, and I would be glad to answer any questions you may have.
Best wishes and welcome to Ireland,
Lauri