All indicators show the Reeds I'm looking for were in SW NY, mainly Cattaraugus County. Betsey was born in Conewango. There are Reeds present on the 1820 and 1830 Census, one with a daughter in the right age range, but I can't find any other connectors. Those Reeds were Daniel Reed & Prudence (Shephard) Reed, but as I stated, there is nothing conclusive to indicate they are her parents, and they don't tie to her uncle & aunt at all.
Her uncle & aunt were Solomon George Wright (1807-1893) & Sarah Sally (Sykes) Wright (1805-1866). They lived in New Albion before Sally died. He was Postmaster at one point, and also ran a mill. The unusual architecture of his house is mentioned in The History of Cattaraugus County. One of my cousins and I have extensively researched the Wrights and the Sykes. There are no Reeds on either side, so we have no idea how Betsey fits in as a niece.
In 1847-48, both Lewis Bullock and Solomon Wright wrote to Betsey while Lewis was visiting the Wrights (Betsey stayed back in IL). Those letters have survived through the generations. Lewis tells of arriving at "Uncle Wright's house" safely and also mentions Aunt Sally and several of their children by name. Solomon starts his letter off "Beloved Niece" and mentions that Aunt Sally is making a rug.
The Bullocks visited the Wrights in Sep 1851. They had with them their two youngest sons, both infants. An early snow stranded them in NY for the winter. Lewis wrote of this in The Christian Palladium in a letter to Elder Oliver Barr. He contracted typhoid and died 10 Feb 1852. Betsey succumbed to the same disease on 4 Apr 1852. That same winter, the Wright's oldest son also died of typhoid.
Lewis & Betsey Bullock settled in Kane and Kendall Counties in Illinois, though records of Lewis performing marriages reach to La Salle, De Kalb and Gallatin Counties, and one of his children was born in Sangamon County. Census and church records, though, have them living primarily in Kane and Kendall Counties. Several of his siblings also settled in the same areas before scattering to Iowa, Nebraska and Wyoming.
Other things we're frustrated about include the lack of graves for Lewis & Betsey Bullock. They died in New Albion. Lewis's father is said to have been buried in Leon (but we haven't found his grave either). Yet no trace or mention of their graves have turned up. We know that most or all of Leon Center was uprooted and moved. It's possible the graves got lost in the move. It's also possible that the headstones were made of wood and rotted away to dust long ago. Betsey, though, is one of our biggest mysteries, and having references to the Wrights being her uncle & aunt make things even more mysterious.
Sorry, I got a little carried away. I hope this answers your questions. Let me know if you have more or want more information. And thank you for inquiring.