Source: Ancestry.com—Theiss Family Tree; Baltimore, Passenger Lists, 1820-1964; and www.findagrave.com.
He and his family immigrated sometime between 1842 and 1845, based on the birthplaces of his children. The Theiss Family Tree site refers to the Baltimore Passenger Lists. These records include arrivals in Baltimore, Maryland between July 1 and September 30, 1843. The list includes Bartholomew Thome, age 30, his wife Catherine, age 27, and their children John, age 4 and Gertrude, age 2. Based on the page number of the list, they probably arrived in September of 1843. Matthias was not included on the list.
In 1850 he and his wife and four children lived in Avon, Lorain County, Ohio, next door to his brother Peter Thome and his family. In 1860 he and his wife and their eight children lived in Avon. His family name was spelled Tomah on the 1860 federal census.
In 1870 he and his wife and six of their children lived in New Bavaria, Pleasant Township, Henry County, Ohio. Their name was spelled Tohma on the 1870 census. Their son Matthias lived nearby with his wife and daughter Mary. In 1880 he and his wife lived with their daughter Lizzie and five-year-old granddaughter Emma in Pleasant Township. Their sons Joseph Thome and Matthias Thome and their families lived nearby.
Their granddaughter Emma (or Anna) lived with the family of their daughter Elizabeth Mary Thome Laubenthal in both 1900 and 1920 in Ottawa Township, Putnam County, Ohio.

Source: Ancestry.com—Theiss Family Tree; and www.findagrave.com.