Do you really need a van? Fuel is not cheap in Ireland. You might want to consider renting a hatchback, folding down the rear seats and taking off the front wheel of the bicycle to put it inside.

Last year (spring 2009) I spent a couple weeks in Ireland using the bike and trains. The rail network will get you just about anywhere you want to go, and you can take your bicycle on most trains. I had a big enough saddlebag and handlebar bag to hold clothing and camera, and I toured from hostel to hostel. I spent a good bit of time in the southwest corner of the country (Kerry, Iveragh peninsula, Beara Peninsula), and spent some time visiting family in the Dublin area.

I brought the bicycle on the plane fully assembled/unboxed, and rode it to and from Dublin airport, which is very easy to do. Check the rules for whichever airline you're using VERY carefully before you try this, and check the fees for bicycles just as carefully. British Airways has about the most reasonable fees for bicycles, other airlines charge up to 150 euro to bring a bicycle.

Bring fenders and good rain gear, the stories about the weather are all true.