Three girls named Bullock are listed as Mordecai students:
Ann Bullock from Warren County (?) attended from early 1816 to the last session with the Mordecais, in late 1818; Richard Bullock is the adult name on her account.
Catherine and Eliza Bullock both attended the Mordecai school in 1809 only. They were probably also from somewhere near Warrenton, because many of the first students at the school were local children.
A Richard Bullock appears throughout the school's ledger for the years Ann attended; there's also mention of a James Bullock in June 1818. There's mention of Ann's father paying a lot of attention (courting) a Mary Turner in 1820 correspondence by the family; and in an 1822 letter from Warrenton, Caroline Mordecai Plunkett reports that "There are several weddings now in agitation among the number is Ann Bullock's she is to be married to a son of Judge Henderson." (Caroline Plunkett to Rachel Lazarus, 7 September 1822, Jacob Mordecai Papers, Duke University)
That last tidbit leads us to Anne E. Bullock Henderson (1804-1883), of Granville County (not Warren), Ashland Plantation, who indeed married Archibald Erskine Henderson (1801-1853) in 1822, in Warren County. Archibald's father was Judge Leonard Henderson (1772-1833), Chief Justice of NC. Archibald was a UNC alumnus, a planter and a magistrate. Their seven children were all born in Granville County, between 1823 and 1845. Looks like she was widowed at age 49, with her youngest child just eight at the time. In 1860, the census finds the Henderson household with 129 slaves.
The other Bullock girls are likely relatives of Anne's, but it's a big family in the area. There's a Catherine Lewis Bullock, b. c. 1802, who married Joseph Newton Sims, himself the grandson of a woman named Sarah Bullock. The wedding was in 1822, in Warren or Granville County. Catherine would have been widowed in 1850, in Louisiana. This Catherine Bullock had at least one son, James Bullock Sims, who was born at Tennessee; and a daughter, Sallie Sims. She also had a sister-in-law named Susanna Sims Burt--and a Susan Sims is listed among the Mordecai students who only attended in 1809, along with Catherine Bullock. So it seems like a decent chance she's the Mordecai student.