The Invincibles went on to become – and remain – the only Australian side to go through an entire Ashes tour unbeaten.
The item, which spent 20 years on display at the Western Australian Cricket Association (WACA) from 1984, will be auctioned on August 15 in Melbourne.
"Few items of cricketing memorabilia overshadow those belonging to Sir Donald Bradman," Leski said.
"Of these, his bats are among the most prized possessions because they were his ultimate stock in trade."
"Together with his baggy green caps, they represent his unique talent that has yet to be matched."
The legendary Australia batsman, who died aged 92 in 2001, played his last match in England in 1948 and retired with a yet-to-be-topped Test batting average of 99.94 despite scoring a duck in his final innings.