I see this is your first posting on Rootsweb, at least under this user name. When you post, sometimes it helps to give the whole story. I'm "assuming" you are looking to find where a relative had lived, was born, died. It might help in this search for Bybee to know just who you seek. The name of Bybee might have been an area named for the resident family. It does not appear to have been incorporated.
The Jefferson Hills Golf Course is at 4074 E 500 N, Rigby
This aerial photo of that area (if the link maintains) shows the golf course and vicinity. If not use Mapquest.com and switch to Aerial map. But, since you've already visited the area, you know what it looks like.http://classic.mapquest.com/maps?city=Annis&state=ID&...
I found the same area on a topo map, but it doesn't show Bybee, which is somewhat unusual to me to not have something like that appear.http://msrmaps.com/image.aspx?T=2&S=12&Z=12&X=53...
The US Geological Survey does not identify Bybee.
The 1930 had no Bybee, 2,504 in Rigby
The 1920 had no Bybee, 2,736 in Rigby
The 1910 had no Bybee, 1,335 in Rigby (Fremont, Co).
The 1900 had no Bybee, 595 in Rigby (Fremont, Co).
The 1880 had no Bybee, no Rigby. (It was founded in 1883, named after William F. Rigby, a prominent early settler and member of the LDS church.
There were no Bybee in Jefferson County, 1880, 1900, 1910. In 1920, there were 23 in Jefferson Co, 8 in Annis, 3 in Menan, the rest in Rigby. In 1930, there were 28 in Jefferson Co. Annis and Menan are north and northwest of Rigby.
The Bureau of Land Management has a database of land patents issued under the Homestead Act (and other Congressional land grant acts). It does not show a Bybee obtaining land in Jefferson County.http://www.glorecords.blm.gov/search/default.aspx#searchTabI...
--Ancestors and Descendants of Elias Adams, the Pioneer. Page 248 shows Green and Bybee families, children born in Grace, Idaho.
--History of William Crow of Virginia and his Descendants in America. Page 212 has Bybee named persons, in Pocatello, ID.
--Our Ellsworth Ancestors. Page 153: Mariam Vilate Ellsworth married Henry Peter Lee, had nine children, #'s 7-9, Lavern Lee, 1911; Vivian Lee 1914; Leola Lee, 1915, born in Rigby.
--Descendants of Luman Andros Shurtliff. Had Bybee born in Bannock Co.
--A History of My People and Yours. Page 380, Monti Mary Lee, born 1903, at Farr West, Utah, married Earnest Polson, June 30, 1924 at Bybee, Idaho. He was born Mar. 26 ,1902 at Taylor, Idaho. Daughters: Rosmary Polson, born May 26, 1905, at Bybee, Idaho; Bonita Jean Polson born Feb 14, 1929 at Shelly, ID.
--History and Genealogy of the Ricks Family of America. Sharon Bybee born 1930 in Rexburg, ID, daughter of Ray Bybee and Margaret Palmer.
Other books identifying the birth of television describe a farm owned by the father of Philo Taylor Farnsworth. It identifies also his uncle's 240 acre ranch near Rigby.http://books.google.com/books?id=VMcNp9zJkXsC&pg=PA89&am...
This one: http://books.google.com/books?id=28cMReggGGEC&pg=PA38&am...
The family of Philo Taylor Farnsworth...moved to a new homestead owned by an uncle in Bybee, Idaho in 1919...
--The BLM Database shows S. Dennis Farnsworth obtaining 160 acres of land in Jefferson County on 6/13/1919. It was located in Township 8-North, Range 36-East, Section 4. I did locate this land but it was quite removed from Rigby, and no Bybee was seen on the topo map.
For this information it appears you need someone more of a historian/genealogist. The Random Acts of Genealogical Kindness has a volunteer in Jefferson Co: http://www.raogk.org/idaho2.htm
Larua does Public Records (library). The library would have local history information about locations.
This book on early settlers might also have what you seek:http://boards.ancestry.netscape.com/thread.aspx?mv=flat&...