The Birth Date is a rough estimate. See the text for details.
Biography
Son of Samuel and and Abigail (Lee) Bush.
He married Mary Fairbanks, daughter of Jeremiah and Mary (Penfield) Fairbanks.
Marriage intentions filed on 25 January 1726 in Bristol, Bristol, Rhode Island.[1]
↑ "Rhode Island Deaths and Burials, 1802-1950," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F869-J88 : 6 December 2014), Richard Bush, 27 Sep 1732; citing Bristol, Bristol, Rhode Island, reference p 11; FHL microfilm 912,787.
Genealogy of the Fairbanks Family in America, 1633-1897, By Lorenzo Sayles Fairbanks [1]
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DNA Connections
It may be possible to confirm family relationships with Richard by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Richard:
Looking over the locations in this profile and also the best secondary source on the family of Samuel Bush [See: https://archive.org/details/jamescoxbradyhis00defo/page/130/mode/2up], I don't see any evidence that he had a son Richard. If there are no objections, I'd like to disconnect Richard from these parents.
There is Bush DNA surname project. See: http://www.personal.psu.edu/faculty/g/a/gah4/BushDNA/B1.html If a male-line descendant could be identified to take the Y-DNA test, they could possibly prove otherwise.