I thought I had heard of Bellevue and it wasn't nice. Found this by googling for the hospital
The name of this famed hospital was once a byword for the horrors of medical and psychiatric care.
it was the one place a New Yorker didn’t want to go, because the chances were you wouldn’t come back.
https://www.atlasobscura.com/places/bellevue-hospital---------
Regarding her birth, if you have a town in Massachusetts or her father's name, you might find her. I found two on Familysearch.org without trying too hard. Unless you are sure of the year. I looked for 1800 to 1808.
Sarah Shipman Warner, March 1805, Hadley MA, father Jonathan
Sarah Burke Warner 8 February 1800, Bernardston MA, father Joel, mother Thankful
If you get desperate, you might trace those two women, to see if you can eliminate them. E.g, did they stay in their town and marry someone, etc.,
If you don't find her at familysearch, you might try AmericanAncestors.org, the site for the New England Hist. and Gen. Society, located in Boston. Or even archives.org for town records, though you would have to know which town. They might have them by now. Massachusetts Town records before 1850 were collected and printed in a series of books and they are probably out there somewhere for free.