There is a student named Eliza Bowell in the rolls of the Mordecai school. She attended for three sessions, 1816 and the first half of 1817. The adult name that may be attached to her account is Abner F. Bowell, and she's linked to Fayetteville.
There was an Abner F. Bowell who died in Fayetteville in 1827, age 50. He turns up in the 1820 US Census as a head of household in Fayetteville, with eleven free white people in the home: a boy under 16, three boys 16-18, three men 16-26, a man 26-46 (probably Bowell himself), and a girl 10-16, a woman 16-26, and another woman 26-45. All the adult males in the household may be explained by Bowell being a shop owner, perhaps a printer, who housed his employees and apprentices. This family historian links the surname Bowell with Bowles/Boles in North Carolina. She also mentions an Eliza Bowell who married a man named Ochiltree.
Taking that lead: This family historian has Eliza Ann Bowell (1802-1865), daughter or niece of Abner Bowell of Fayetteville, marrying Archibald Ochiltree (1793-1832), in 1818. She was widowed at thirty, and seems to have moved to Texas later in life, to be with one or more of her children. Looks like she may have had a son Hugh Ochiltree (1820-1891) who was born in NC, but was a lawyer and community leader in Madison, Texas. (Here's a picture of Hugh.) Ochiltree County, Texas, on the Oklahoma border, is named for Hugh's cousin (Eliza's nephew?) William Beck Ochiltree (1811-1867), who was also born in Fayetteville. The DAR record for Hugh Ochiltree's daughter Arabella Ochiltree Bancroft (1870-1924) has "Eliza A. Powell" as his mother.
So.... Eliza Ann Bowell was a Fayetteville girl, born 1802. She went to school in Warrenton when she was 13-14, for a year and a half, then married at 16 to Archibald Ochiltree. They had at least one child before Eliza was widowed 1832, at age 30. She may have moved to Texas and died there in 1865.