I was in Dublin back in June. I had about 8 hours before meeting my group. I rented a bike from The Lazy Bike Tour Company (they also do tours on "electric assist" bikes), I rented a cruiser bike. BTW- no electrical assist. I rode away from the shop and came to the realization that "they" were driving on the opposite side of the street. I had no idea what sites to see. and a cutesy tourist map of the area. Then....
a tour bus passed me and I followed the tour buses all around Dublin. One- I saw the sites of Dublin, the buses never went over 15mph and it was a circular route. Great day of riding.
I saw a ton of road bikes in Western Ireland. I didn't ride myself while there, but the owner of the cabin we rented was an avid cyclist.
The other thing I noted was the prevalence of reflective safety vests on cyclists, horse riders, and even pedestrians travelling on country roads at night.