There was a student on the rolls at the Mordecai school for four sessions (1815-1816) named Margaret Burcher, of Norfolk VA. The adult names attached to her account are Mr. Geddis and Capt. Samuel Vickery.
Margaret Burcher was at the school long enough to make appearances in Mordecai correspondence. "Eliza Armistead, Miss Burcher, & Miss Taylor arrived today from Norfolk," Rachel Mordecai wrote to her brother Samuel on 25 January 1816; the following year, Solomon Mordecai wrote to his sister Ellen that "I also met with Margt. Burcher; she is a diminuitive little figure, in no respect altered in appearance since you saw her, but do not say so to any of her Norfolk acquaintances, I am told it mortifies her not a little." (Solomon to Ellen, 15 July 1817; both letters quoted here are in the Mordecai Family Papers, Southern Historical Collection at UNC-Chapel Hill). Solomon wrote again to Ellen on 24 November 1822 to say that "M. Burcher is improved." Margaret was "keeping school" in Hampton in the summer of 1828, and Ellen had an idea of Margaret becoming an assistant at Caroline Mordecai Plunkett's school, saying that "She is sensible & no doubt teaches in the same way that you do, would probably be glad of the situation ,and it would be so much more agreeable to have a female than a stranger male for an assistant." (Ellen to Caroline, 27 July 1828, Jacob Mordecai Papers at Duke). But Caroline was not interested in pursuing the plan (Caroline to Ellen, 2 August 1828, Jacob Mordecai Papers at Duke).
Turning to the online resources: There's a Miss Margaret Burcher buried in the cemetery at Christ Church, Norfolk VA, who died 19 September 1855, with a note that she's among those who died from yellow fever that year. In death, the schoolteacher became more newsworthy than she ever was during her lifetime: her name appeared in the New York Times on 24 September 1855, as one of the epidemic's many Norfolk fatalities (one Norfolk newspaper at the time estimated that 2000 yellow fever victims were buried in a ninety-day period).
The only other mentions I find of her include a note in the finding aid for the Cocke Family Papers at the University of Virginia Library; she wrote to John Hartwell Cocke about a school-teacher's position in 1840. There is also mention of Miss Margaret Burcher in the Galt Papers at the Special Collections Research Center, in a child's letter written 1846, from Caroline County VA.
So it looks like Miss Margaret Burcher worked as a teacher for much of her life, and died in her 50s in a terrible epidemic. Because that story doesn't include marriage or children, she's nobody's ancestor; being a lifelong single woman makes her less likely to appear in traditional genealogies (concerned with linking ancestors and descendants). But still, where was she born? When? To whom? How long did she teach?