There were six Ann Bridsons on the IGI between 1847 and 1851.
Two died early.
Two others, I cannot find in a census:
Aug 1847 christened in Douglas daughter of William Bridson and Catherine,
Ann Jane 1849 christened in St. Marks
A fifth ANN christian, born in January 1850 in Patrick is in the 1871 census under her maidem name.
That leaves Ann Jane christened in Malew July 22, 1850.
The IGI gives her parests as Thomas Bridson and Ann.
Thomas Bridson married Elizabeth Bridson on June 20 1848 in Malew. i suspect that Ann is a transcription error.
Thomas, Elizabeth and Ann are in Malew in the 1851 census. Thomas is a tailor
In 1861 Thomas is a widower with Ann 11, and John 9.
In 1871 Thomas 48 is still a Tailor in Castletown and has a new wife Esther 38 and two new children, Mary 4 and Edward 10 months.
This is the most likely of those six in the IGI.