Welcome to Ireland Reaching out and apologies for the delay in getting back to you.
As you say Patrick and Catherine married in Shrule on 17-Jul-1845. Patrick's home address (townland) was recorded as Glassbally. I could not find any baptism records for children born to Patrick and Catherine in Mayo or anywhere else in Ireland.I also searched for the marriage of a Bryan or a Bernard to a wife first name Honor/Honora without success. If you know his date of death you could see if there is any further information on a death record or obituary. I couldn't locate a Patrick Mulloy on the Tithes either and the family were likely gone from the parish by the time of the Griffith's Valuation in the late 1850s.