It looks like the William who was the son of James S. Bodine is the William Bodine who is mentioned in a note on a 1910 Census of Ewing Township, Franklin County, Illinois I found at Rootsweb. A Euphemia Bodine is in that census. Her parents are noted as William Bodine and Mary Ellen MYERS ROGERS. That William had a sister named Euphemia.
The file from Sam Bodine says this William was born in 1837 in Jefferson County, Illinois. That may or may not be accurate.