My best guess is that her parents are Patrick Blanche and Mary Bird.
There is a baptismal record for Bridget Blanche, daughter of Patrick and Mary, who was born 18 February 1822 in Shemogue, NB and baptized 5 May 1822. The 1861, 1871, and 1881 censuses put Bridget Savage's birth date at about 1821-1822 in New Brunswick, which fits with this.
Both of her parents were born in Placentia and must have come to New Brunswick about 1818, as their oldest daughter, Dorothy, was born in Placentia but baptized in Shemogue.
Patrick Blanche was the son of Michael Blanche and Bridget Fitzpatrick, who were presumably married in Placentia and came to New Brunswick with their children. Michael may have been a son of George Blanche, the tavern keeper at Placentia, but I don't have any proof of this. The Blanche family goes back a long ways in Placentia.
Mary Bird was the daughter of Joseph Bird and Dorothy Corbin. I think that Joseph may have been born in England, and Dorothy was probably born in Placentia.
These are the children I have found for Patrick and Mary:
Dorothy Blanch (1818-?)
Dorothy Blanch (1820-1837)
Bridget Blanch (1822-1906)
Anne Blanch (1824-?)
Sophia Blanch (1826-?)
Michael Blanch (1829-1837)
Joseph Blanch (1830-1872)
Mary Esther Blanch (~1832-?)
Gertrude Blanch (1835-1837)
Dorothy Blanch (~1838-?)
Elizabeth Blanch (1843-1935)
John Blanche (1844-?)
They may also have had a son named Bernard or Barnabus, though I have not found anything about him.
There's lots of information on the Blanche family in the Drouin Collection of church records here on ancestry.