Aurra Sing joined the Jedi Order but never made it past the rank of Padawan. She left the Order to become a bounty hunter. It’s not stated in Canon why she left or how she became a bounty hunter. However, it’s elaborated on a lot more in the Legends continuity. She was abducted by pirates and then sent to an assassin training and then became a bounty hunter afterward. So, Aurra Sing was never a fully-fledged Jedi, but she had a bit of Jedi training.