I checked out the 1880 US Census on LDS/Family Search (free site on the internet) Dr. Robert Bright was b. 1829 TN - and it says father b. KY and mother b. TN - so you are looking for a Bright born in KY I would make an estimate that the father was about 20 years old when son Robert was born - so his father probably born about 1809 in KY - and must have had SOME money because the son studied to be a doctor. The name of one son of Dr. Robert Bright was Gustave, b. 1862 TN.That may be a clue as to relatives.
On www.worldconnect.rootsweb.com there is listed: William Gustave Bright b. 15 January 1862 Brazile, TN died 16 Nov. 1949 Lancaster, DALLAS CO, TX buried Oakwood Cemetery, Austin, TX Father: John R. Bright b. @ 1840 TN
That could be another clue - perhaps the father of John R. Bright is the same as that of Robert Bright b. 1829 TN.
This is not my family, but others have helped me a lot. I hope this information will be helpful.
Maybe the obituary of William Gustave Bright would give some information about his parents or other relatives that would help.I don't know the size of Lancaster in Dallas County, TX, but a good library in that part of the state should have 1949 obituary information - or a newspaper, also.Certainly the Oakwood Cemetery in Austin, TX would have information on what Funeral Home took care of the burial. That should be a good help for information.