We are arriving in Dublin on a Tuesday at about 12:00 noon in early March on a connecting BA flight from LHR following a BA direct flight to LHR from Nashville. We will not have checked bags.
What is a good estimate of how much time to allow to clear customs in Dublin as we will be booking a bus that afternoon from the airport to Galway?
Also, what will be required of us upon arrival that morning at LHR as far as Customs and clearing security there before continuing on to Dublin?
This website will give you detailed information on what to do at Heathrow:
https://www.heathrow.com/connecting-flights
If traveling on a US Passport you will go through immigration at both Heathrow and Dublin. Security at Heathrow as well.
How long it will take in Dublin is anyone's guess.
I'm not sure you need a reservation for a bus to Galway from the airport. Especially in March.