After the initial talk with Quella, Shiro was told to wait for her sister's responses after they figured out what they should do with her new found power. With so much mystery behind it, they needed to test out its capabilities before trying it against the Ancient Terror.
With Shiro needing to earn money for the weapon and armours as well, the monsters on the bounty board were perfect test subjects.
Since one divinity rank monsters were already easily killable for Shiro, their best subjects were those with two divinities. One of the ones that Quella suggested Shiro to try was the Gorgon since she had a bow and arrow.
Remembering her experience with the Gorgon back on Earth, Shiro rejected it since she didn't want to be turned to stone.
She had thought that she could just ignore their gaze and she'll be fine but no, they would petrify her even without making eye contact.