This Ann Bodine appears to be the Amy Bevier who is mentioned below in several records. That is a guess at the moment, but the evidence is pretty good. See more on this below.
There is an Amy Bevier listed in the household of Ann's mother, Susanna Bodine, in the 1850 Census of Cass Twp., Richland Co., OH. Amy was 31 and born in Ohio. Her age does kind of match this Ann. Amy had two children listed: Russel Bevier (age 8, b. Ohio) and Susan E. (age 4, b. Ohio). Here is that info:
Susanna Bodine 53, NJ
Hannah M. Bodine 15, NY
Martinn (fem) Bodine 14, NY this was hard to read
Laura 12, NY
Amy Bevier 31, Ohio (same household, probably a daughter)
Russel Bevier 8, Ohio (note the family name)
Susan E, 4, Ohio
Also in the 1850 Census, Amy Bevier is found in the household of Thomas S. Bodine. Here is that info:
Ripley Twp., Heron Co., Ohio:
Thomas S. Bodine, age 24, hotel keeper, b. NY
1/12 year old daughter listed as Namelus
Ann Beverie, 31
son Russel, 5
This was recorded on Nov. 8, 1850. She must be the same as Amy Bevier and children Russel and Susan recorded as living with Susanna, widow of Peter on 16th of Sept., 1850 in Cass Twp., Richland Co., OH.
LDS says she is "of Lancaster, PA."
From Ronny Bodine:
From the death record of Eliza Elizabeth Sykes:
Born Battle Creek, Michigan. Died 19 June 1932 Plymouth, Richland County, Ohio, aged 82 years, 2 months and 17 days and buried in Greenlawn Cemetery. Widow of Wm. H. Sykes. Daughter of Joseph Bevier, born Plymouth, Ohio and Anne Bodine, born Plymouth, Ohio.
From Ohio Federal Census Records:
1850 Cass Twp., Richland County: Susanna Bodine 53 NJ, Hannah M. 15 NY, Martena 14 NY, Laura 12 NY, Amy Bevier 31 NY, Russel Bevier 8 OH, Susan E. Bevier 4 OH.