From "The Tyler Genealogy: The Descendants of Job Tyler, of Andover..." volume 1, page 274 we are informed that Hannah is the daughter of Jonathan Bartlett and a descendant of Josiah Bartlett, a signer of the Declaration of Independence. (link - https://books.google.com/books?id=9Zs-AAAAYAAJ&pg=PA274&lpg...)
I have looked through Amesbury (Mass.) VR for a Jonathan born at roughly the same time as Josiah. Hannah was born in 1768 so Jonathan could have been born as late as 1735.
Any help in finding her parents would be greatly appreciated.