Sharon, the website you referred to is in error. The list of families of indigent soldiers had nothing to do with the Freedman's Bureau, which was a postwar Federal agency charged with protecting the interests of former slaves.
The list you referred to was a civil responsibility of the county. Under the requirements of "An act to provide for the relief of needy and destitute families of soldiers in this State," approved by the Arkansas legislature on December 1, 1862, the county courts were supposed to prepare a descriptive list "from personal knowledge and information and careful inquiry and examination that all of said families are needy and destitute within the spirit and meaning of the act." Qualified families were supposed to receive a small stipend for food and clothing.
There are several surviving descriptive lists from various counties, dating from February 1863 to October 1864. I don't know the date of the Bradley County list, but it should be available in the records of the county court.
The soldier "status" section of the lists are unreliable. They were often based on word of mouth, so a soldier listed as "supposed to be dead," might actually be a prisoner of war, etc.