Chessebelle didn't know much about the Zero Division. Obviously, like any shinigami in the Gotei 13, she knew their purpose and their duties but not much else. Most people of her generation in the Gotei didn't know or even hear of the Zero Division's members until Kirio Hikifune was promoted. The only reason Chessebelle knew this was because of her placement into Squad Twelve shortly after Hikifune's promotion to the Zero Division.
However, after snooping about the twelfth division's records, she found another name of a Zero Division member: Senjumaru Shutara. It wasn't exactly up to code for her to be rifling through the records, but once she found the name she couldn't stop her investigation. She kept looking for instances of the woman in the history of the twelfth division, eating up every bit of information she could get her hands on.
Apparently she was an important contributor to the twelfth division during her days, even creating a scale used within the division for years to come named after her. Chessebelle became obsessed with the image of her, always finding herself wanting of more information she hadn't yet stumbled upon about the mysterious Zero Division member.
While she wouldn't admit to becoming infatuated with the powerful woman, it was obvious that whenever someone asked for use of the Shutara scale she would perk. She seemed to be expecting information on the woman when her sacred name was ever uttered aloud.
She longed to become someone like Senjumaru Shutara.