Hopefully another biker will answer this in a bit more detail than I can, but I can help on a few things. Ireland is small. Very small. A good days ride will go from the top to the bottom, or from one side to the other AND back again.
Also, depending on the time of the year you come, if it's off peak you can get accomadation in just about any town quite easily without pre-booking. This means you can travel with a very flexible schedule. We use a lot of Bed and Breakfasts, and these are rooms in peoples houses, or even larger spots with 5 or 6 bedrooms to rent. They usually will have a driveway to park a bike. unlike the USA (Moab to be specific), Irish bend and breakfasts are not boutique expensive and plush places to stay, they are more basic - very much how normal people live. Hostels are fine too but can be noisy.
Routes: The best things to see are all round the coast. Some things are the big attractions, like the cliffs of mohar Tourist Attraction in Ireland, Things to Do in Ireland - Cliffs of Moher
, or the giants causeway, and these can be seen easily by just riding up to them. A full loop of the coast is a good plan to start from, and then refine it depending on how much time you have. 2 weeks would probably do a lap at a reasonable pace and getting to see a good few things, 3 weeks would be better. Any less than 2 weeks, then just concentrate on counties kerry, clare, galway (i.e. the west coast).
And a great thing to include is the hubb meeting in eniskillen, held each year. You can find details here on the hubb, and if you put that into the start of your trip you'll get loads of bang-up-to-date info when your there.
Also, what sort of stuff do you like to see? cities? Countryside? bit of a mix? And how long do you plan to travel for?
Depending on when you go, and when I get back from South America, I can offer you somewhere to stay just outside Dublin.
Very proud to be Irish :-)