There are very few Bauers in Ohio prior to 1850, and most of them are in the Cincinati area.
What about alternative spellings?I have found four different spellings of one family name during that time period in Ohio. There are lots of "Baer" families in the Paris Township area of Stark Co. where I do most of my research.
For instance there is a John Baer in 1850, but he was born around 1820 in PA, married to a Nancy, who was born in Ohio. Maybe you are looking for his parents? I think most German immigrants to Ohio came through PA.