I am flying to Dublin arriving March 13th am and departing March 20th. Would probably like to see 3 counties...one being Donegal as I have heard by many it is one of the most beautiful in Ireland. I have traveled once before to Ireland a long time ago. It was a tour of the South but my boyfriend has never been to Ireland period. I am looking for a way to get from one point to the next without driving and without paying an arm and a leg for a bus tour. I have used Shuttle buses in other countries where they just pick you up and take you to next hotel for a reasonable rate in other countries. Is there any such animal in Ireland. Can't seem to come across what I am looking for. I have airfare booked and plan on booking my hotel myself perhaps thru priceline to save cash. Any ideas?

At risk of not answering the question you've asked, can I highly recommend a car if you don't have a particular reason to avoid driving? One of the joys of travel in Ireland is being able to explore roads you've just discovered, or meander off course to admire a view or have lunch in a pub. Often the journey from one town to the next is the best part of the trip. Just looking at the Hertz website (which my weird and selective internet filter here at work will let me view), I can see a car for March 13 - 20 for 189 Euro, which comes down to 27 per day, or 13.50 each. I'm positive you could do better via a consolidator. By the time you've paid for transport out to see various sights plus shuttles from hotel to hotel, I'm pretty sure you'd do better with a car.
If driving is impossible for you, then be assured that Ireland has a very reliable train system, and the buses are also pretty decent. It's well set up for tourism, so you'll be able to book day tours to see attractions and so on. You may find that taking the train or bus from place to place is just fine, combined with the occasional short taxi ride from the station or terminus. If this is the way you're going, obviously having an eye to the sort of luggage you're bringing will be helpful.
Have a great trip!

The national bus company is Bus Eireann www.buseireann.ie, their network is extensive around the cities and large and medium sized towns in Ireland. Donegal is largely rural save for the towns Letterkenny and Donegal Town and the county as as whole is not best served by public or private transport. Donegal is one of the most beautiful parts of the country and is best explored by car or bike if you have the time. Donegal is not served by our rail network.
I know Donegal quite well, so if you are looking for advise on places to visit let me know if you want any help.
Enjoy!