Hi Richard,
First of all, May is a great time to visit whether by public transport or car!
Probably the reason for the difficulty in finding a suitable service is that from Kenmare to Dingle, there is no direct service so sometimes the option won't appear. Transport for Ireland has a helpful journey planner that we use that will show multiple service providers from end to end. So, please have a look at this search from
Kenmare to Dingle for the buses from Kenmare to Killarney to Tralee to Dingle. The provider is Bus Éireann so you can search the individual services on their website, they have a rolling schedule so exact times won't be available until closer to next May.
Similarly, there is no direct service from
Dingle to Galway, so again Transport for Irelands search highlights the bus numbers required from Dingle to Tralee to Limerick to Galway! Again the services are all from Bus Éireann so you will be able to look at the times there. It will take the best part of 6 hours or so for this journey but the benefit is that you are able to see some of the wonderful countryside through the windows.
Hope this helps with your travel plans, we would love to hear what you have planned for your time in Dublin, Cork, Kenmare, Dingle and Galway!
Regards,
Martin