He was the younger of two children who lived to adulthood. His older brother Will was five years older than he, and moved from Kansas to Jacksonville, Florida to start a furniture business in 1874, just as Bion enrolled at the University of Kansas. Will spoke highly of Florida's moderate winter, so the following year, his parents journeyed to Jacksonville to visit their oldest son. Sarah Barnett suffered from neuralgia, but her health improved during their time in Florida, so the Barnetts returned to Kansas, liquidated their assets, and relocated to Jacksonville in March 1877. Bion, who was a college senior, withdrew from school to join his parents three months before graduation.