On findagrave.com, there are 4 Roths entered for Fairfield County:Alice M., Bernard G., George E., and Henry L.George E. Roth is the only one who might be someho0w connected because he was born in 1858 (the rest are too late).A search for his death certificate lists him as the son of John Roth and Hannah Ranch.
foorgenealogy.com only lists 2 Roths for Bloom Twp., Fairfield Co.--Eva Catherine and James--but doesn't give dates or much other information.
Looking on familysearch.org, I see death certificates for two possible children of your Jacob & Anna--William A. Roth (b. 18 Sep 1860, Licking Co., OH; d. 19 Mar 1928, Kenton, Hardin Co., OH) & Mary S. Roth Cox (b. 7 Jun 1857, Hardin Co., OH; d. 6 Apr 1931, Kent, Hardin Co., OH)--but I don't see one for Caroline Roth Bailey.
There are, however, many Baileys listed in Fairfield County on findagrave.com, most of which I've entered myself.You might be able to find information on her husband's family.