Bonemer was promoted to Double-A Birmingham on Sunday, Scott Merkin of MLB.com reports.
Bonemer will move up a level in Chicago's minor-league farm system, joining the Double-A squad after posting a .238 average with 18 home runs, 43 RBI, 52 runs and 10 stolen bases over 223 at-bats in 61 games with High-A Winston-Salem this year. The 20-year-old is considered to be the top overall prospect for the White Sox, and he'll look to build off of his impressive power numbers at the next level.