Some very Jane Austeny student names this time!
Eliza Anne Bennett attended the Mordecai school for both terms in 1818, with Richard E. Bennett as the adult associated with her account, and Petersburg VA as the place name.
Jane Bennett attended the Mordecai school much earlier than Eliza Anne, for six terms, from the beginning of 1811 to the end of 1813. She is also listed as being from Petersburg VA, but her account is associated with a Thomas Bennett. There's further note that she must have been married by 1827 (because the Mordecais mentioned her as married in a letter that year).
So who are the Misses Bennett? Hmmm... First thing I find in the genealogy forums is a Jane Grey Bennett marrying a Thomas N. Lee in 1823, in Petersburg VA. Elsewhere she's Jane Gray Bennett Lee, born 1802 to Sarah Elizabeth Wall (1778-1847) and Thomas Bennett, named for her maternal aunt Jane Gray Wall Shore Haxall (1766-1831), married to Thomas Noble Lee. She seems to have had a daughter Jane Gray Lee who died in infancy in 1824. Through her mother's family, Jane Gray Bennett was related to many of her classmates, including Olivia and Margaret Barrow. (The Grays were in Virginia beginning at Jamestown c. 1616, so many of the planter families of the area could claim Gray kin.)
Jane's husband Thomas Noble Lee was an Englishman, a tobacconist born in Yorkshire, who "held thirty or more slaves in the tax assessments for 1836 and 1838" and was a member of the PBMA (Petersburg Benevolent Mechanics Association), according to L. Diane Barnes, Artisan Workers in the Upper South: Petersburg, Virginia, 1820-1865 (LSU Press 2008). He was also a director of the Petersburg Savings Institution when it was founded in 1837.
None of these leads turn up the Eliza Anne Bennett who also attended the Mordecai school. There's no reason to think the girls were sisters--different men paid their accounts, and they didn't attend school together. But they're both from Petersburg, and they may have been related somehow. And none of the leads on Jane Bennett give any clue of her life after the mid-1820s. I'll dig up the Mordecai letter about her from 1827 to see if that sheds any further light on her story after getting married.