My family also came from Co Galway. First find what parish Bullaun is in. Then you can check if the parish registers survived, and if they start early enough to capture your family. You may also find the head of the household listed in the Griffith Primary Valuation of the 1850s or the Tithe List of the 1820s.
Be open-minded about spelling variations. Kane is interchangeable with Cain, Caine, Kane, etc., all variants of the original Irish clan name O'Cathain.Ypu may find your family listed under any of these spelling variations.