I've cycled Ireland 3 times. 2 times on my own, upsupported, and once with 4 friends. For the group, we rented a vehicle for support. Even with 5 of us, we got along with 1 small economy car. We simply rented a rack for it from the the car rental company. Of course, we never used the car for all of us + bikes, one person was the designated driver, and we had the option for up to 2 + bikes to ride. We used the car to travel around in the evening, etc. In any case, you certainly don't need a van, and a large vehicle is difficult on Irish roads.

With only 1 week, you are best off doing some research on where you'd like to ride, so you don't waste time in unprofitable messing around. I don't think your plan is necessarily a bad one, but driving in Ireland can be slow, and if you think you're going to drive 100 miles every day and get in a good day of riding, you're mistaken. On our trip, our driver was constantly surprised at how we cyclists covered ground nearly as fast as she did. Average driving on scenic Irish roads will go at about 35 mph--believe it! Don't plan on covering the whole country, but 1 or 2 sections of it. You really need to decide what parts of Ireland you want to see.

If you were to use public transport, you could get to many places from which you could ride some nice areas, but public transport will often not take you to the remote scenic areas themselves.

You say you plan to use hostels. That's fine, and the location of the hostels will dictate the areas you ride in--there are lots of hostels in Ireland. If you really mean B&B, that's also fine, and as someone said, it will cost about 35E/night for an average B&B.

Also, if you haven't checked into car rental rates, be prepared for a big shock. It's extremely expensive in Ireland--another reason for a small car. Be sure to check into insurance, which is not the same as in many other countries.