The Church of Ireland (equivalent to CofE / Anglican) parish is the same as the civil parish in this case, but I dont see any listings for historic records for this parish. I'll check further later on...
The free index on RootsIreland pay-website shows just one Bulfin baptism between 1831-1841 in the records they have for Co. Offaly - but it's seems to be a child named Mary. Haven't worked out the parish/denomination or the father's name - but it doesn't match for William...
Shane