I have discovered almost nothing about my Bradshaws before their arrival in Tennessee from Virginia with a possible stopover in North Carolina. The possible North Carolina stop was very brief since some of my Bradshaws reported themselves as born in Virginia. The first Tennessee stop was probably in Montgomery County since Richard Bradshaw and Joseph Bradshaw showed up there for the 1820 census. They were still there for the 1830 census but must have moved while the census-taking was ongoing since they were also listed in Henry County in 1830.
I do not know the name of Richard's and joseph's and their siblings' father but will speculate a bit. He may have been named William since Richard and Joseph named the oldest sons William, but he may have instead been John. John Bradshaw was listed as head of household two pages before Richard and Joseph on the 1820 census in Montgomery County, however, he may have been either the male over 45 years or the male who was at least 26 but not over 45. If John was the younger male, the older was possibly the father and may have been named William. John was apparently deceased before 1830 since I have not found him on a census after 1820. Although I have estimated his death date as 1825, it may have been a few years earlier or a few years later.
A John Bradshaw was listed on the 1810 census in Goochland County, Virginia. (See below.) He was over 45 and seemingly had a wife over 25 and not older than 45. They had three young males and two young females in the family with one probable son at least ten but under 16, two probable sons at least 16 but under 26, one probable daughter under 10, and one probable daughter at least 16 but under 26. This fits with John as the father in the 1820 census in Montgomery County, Tennessee, if Richard and the brother whose name is uncertain were the males at least 16 but under 26; however, the finding of a John Bradshaw still in Goochland County for the 1820 census does not support our hypothesis that the Goochland John and the Montgomery John were the same.
My research has followed two Bradshaw groups that originated in Virginia and settled in adjoining areas in western Kentucky and western Tennessee, Graves, Kentucky and Calloway County, Kentucky, and Henry County, Tennessee. My family is the Tennessee group. Donald Bradshaw has covered the other family group well.
1810 Goochland, VA, page 420: John Bradshaw 01201 // 10101
1820MontTNp226: John Bradshaw 001011 // 01010; near Richard and Joseph, who were on page 224
"Virginia, Vital Records, 1715-1901", FamilySearch (https://www.familysearch.org/ark:/61903/1:1:68R3-XW6L): Entry for marriage of John Bradshaw and Ann Salmon, 7 Mar 1795. My Bradshaws and the Salmons from Halifax County, Virginia, were still neighbors in Henry County, Tennessee, and Calloway County, Kentucky while I lived in the area from 1937 through about 1970. This page shows some documents about the families.
Richard Bradshaw, Book 14, p. 443, 22 Jun 1789: Richard Bradshaw purchased 212 acres on Jeremiahs Fork from William Wood Note 1
Richard Bradshaw, Book 14, p. 445, 22 Jun 1789: Richard Bradshaw purchased 192 acres on Lawson Creek from Wm. S. Traylor, Sr. Note 1
Anne Bradshaw, Book 20, p. 435, 22 April 1805: Anne Bradshaw, wife of John Bradshaw relinquished her right of dower to 96 acres sold to James Warren.
John Bradshaw, Book 20, pp. 84-85, 27 Feb 1804: John Bradshaw of Halifax County purchased 96 acres on the south side of the Dan River and on Butram Creek from Richard Bradshaw
John & Anne Bradshaw, Book 20, pp. 434-435, 24 Dec 1804: John Bradshaw of Halifax County sold 96 acres on both sides of Butram Creek bounded by Thomas Payne, Lipscomb Ragland, William Bradshaw & Richard Bradshaw to James Warren All Anne and John lists: Note 2
William Bradshaw, Book 20, pp. 83-84, 18 Feb 1804: William Bradshaw of Halifax County purchased 96 acres on Butram Creek from Richard Bradshaw Note 2
Thomas Bradshaw, Book 16, p. 407, 27 Jul 1795: Thomas Bradshaw of Halifax County purchased 110 acres on Bookers Road from Thos Spragins estate 2
Note 1: Information posted online by Mark Arslan
Note 2: Records, Halifax County Courthouse, Halifax, Virginia