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Many of the RC parishes Co. Galway do not have records back to c1815. I did search on the subscription site Roots Ireland for Co. Galway and the only available record was in 1821 in Tuam. See transcription below. You will need to ascertain the names of the parents of Bartholomew (f possible) in order to confirm this record.
You may want to add Bartholomew to our XO Chronicles site https://irelandxo.com/ireland-xo/history-and-genealogy/ancestor-database
Name:Bartholomew TulleyDate of Birth:
Date of Baptism:13-Aug-1821Address:Not RecordedParish/District:TUAMGender:MaleCountyCo. Galway
Father:Gill TulleyMother:Margaret NowlanOccupation:
Sponsor 1 /
Informant 1:Thomas LynotSponsor 2 /
Informant 2:Ellen Green