First Appearance: TBFGK 99
Caesar Borgata and Bunny have a secret relationship. It is unknown whether Don King is aware of this, but Caesar and Bunny seem to go to extremes to keep it hidden, to the point where Caesar flirts with Dewy Tulips in public. Bunny enjoys bubblegum and is quiet even by thinkamancer standards.
If Caesar leads a coup d'état against Don King, Bunny's support would be crucial in coordinating the revolutionaries and feeding misinformation to the loyalists. That may be why he keeps the relationship secret.
Since Bunny is a Thinkamancer, it's possible that her real loyalty is to the Great Minds that Think Alike. Since the Great Minds seem to be trying to use Parson to attack Charlie, Bunny might encourage Caesar to ally with Gobwin Knob, if Caesar takes power, and if Bunny is really loyal to the Great Minds.
Real World References
Her name may be a reference to the traditional "bunny eared" television antenas.
Her name may be a reference to the vampire rabbit Bunnicula from the James Howe children's book series.
Her name may be a reference to the telepath Bunny from the Babylon 5 book trilogy, The Passing of the Techno-Mages.