Stephen,
I'd wing it for a couple of reasons. And relish the experience.
One, it adds a bit of serendipity and adventure to the trip. With over 2,000 B&Bs in Ireland and Northern Ireland, there are many gems waiting to be experienced and more than enough to go around - even in the high season. When you arrive in a town, just look for the ITB (Irish Tourist Board) approved signs with a shamrock out front and start knocking on doors. That assumes you have a definite day's end destination in mind or don't mind overnighting in any given village or town you happen to like. Alternatively, if you have a B&B listing of whatever kind with you, call ahead that morning or afternoon to reserve. The tourist board offices will also do that for you, but with a fee attached. Either way leaves you with flexibility and the option to change your mind about where to go on any given day.
And two, in nine, multi-week trips all over Ireland between July and September - all by bicycle - we've had difficulty finding a room for the night but once - when we arrived in Westport, County Mayo (a lively, popular commercial town) on a weekend. We had to make over a dozen calls to get a room, which was but a five-minute walk from downtown. But on the more than one hundred fifty other nights we've spent in the Republic and the North over the years, we never had to inquire at or call more than two or three B&Bs in any city, town or village to have a place to lay our heads.
An aside: While bicycling in Egypt, we once found ourselves locked out of rooms in a good size town along the Suez Canal because of a convention taking place there. Even though we were camping 99% of the time, it was late and we didn't feel like setting up camp in the desert that night. We eventually ended up asking about accommodations at the police station (the chief even sent two officers out to look for rooms - unsuccessfully as it turned out) and getting a ride from the chief to a hotel a friend of his owned in a larger town twenty-seven miles south. That kind of hospitality rivals what you'll find all over Ireland.
The other caveat - aside from reserving in advance in popular places like Westport and Galway on the weekends - is to be aware of any major event - music festival, horse race, hurling match, etc. - taking place and plan accordingly. Even then, despite seeing no vacancy signs all over and hearing of heavy bookings because of a concert along the west coast of County Donegal, I found a lovely B&B with a spacious room overlooking the ocean. You never know.
Slainte!