I'm not related to this Bush family, however, have been researching Eaton County, Michigan, ancestors for years.
It appears that you have already seen the US Census. Try also www.familysearch.orgUnder the menu "Search Records" try the Record Search Pilot and once the window appears, input "Bush" into the surname box and then begin to type "Eaton, Michigan...into the "Location" box.The program then will prompt you to select "Eaton, Michigan, United States"There are a ton of Bush surname events in Eaton County, and that should give you dates and some marriages.
Also, go here...http://www.eaton.migenweb.net/eatontoc.htmhttp://www.eaton.migenweb.net/eatontoc.htmand scroll down until you find a small search window.Type "Bush" there and a ton of information pops up.In fact I see that Benjamin T Bush is interred in the Delta Center Cemetery.
Also, at that same page, click on the very first top link to a map of the townships.It is helpful to understand the county, which is fairly small and square and the townships are 4 twps x 4 twps (16) and that Delta Twp, for example, is right next to Clinton County.So, be sure to check neighboring counties.
The largest city near Delta is Grand Ledge one twp to the west, Oneida.
To look for living cousins, I've done this a number of ways.For example, in one of the things that pops up when you search Bush is an obituary of someone who passed away in Texas, and it gives the place.Obituaries are great for finding living people..."so and so was survived by..." maiden names, and sometimes places.The next step is to then go to www.dogpile.com and use the "white pages" and search phone numbers.So, go to the input windows, insert "Bush" into the last name window, and then Grand Ledge, Michigan and see what pops up.You will find yourself sometimes dialing a few numbers.I've met living distant relatives this way, introduing myself as a family genealogist and asking if they know of a member of their family who is sort of the family historian.I did this with all children of my ggg-grandparents Sheldon very successfully.It took a little time and a few long distance calls, but it worked.
Best regards, and good luck with the chase.
Jack L. Sheldon, CPA Mesa, AZ (formerly of Owosso, MI, with 3 generations of ancestors in Walton Twp., Eaton County).