I’ve just found a 1833 baptism for Bartholomew:
12 July 1833, Myshall Parish
Barth Brein
Son of Barth Brein and Catherine Finn
He wasn’t Michael Brien’s son then but could have been his nephew. I’m almost certain this is the right family though because there was also a Bridget Finn who was present at the 1853 marriage of Ann Brien, possibly a relation of Bartholomew’s mother?