The only strip Binky Betsy appears in is one where Calvin hoped to make a quick buck and held her hostage with the ransom price of $100.
Susie did not take kindly to that and while Calvin was busy searching for the ransom money she left, as revenge, she stole Hobbes after having left a note that read, "Now we're even" instead.
When Calvin was confused about what the note meant, he went to ask Hobbes, only to find that Susie took his tiger companion.
Calvin had tried several attempts to get Hobbes back. He tried to get Hobbes to bite her. He chased Susie, but couldn't catch her. He also tried to drill Susie's door open.
He later went to return the doll, but Susie says she had grown fond of the tiger and refused to give him back. Eventually, Susie gave in to Calvin's pleading and traded back Hobbes for Binky Betsy and a quarter.
Once Calvin walked up to Susie when she was playing with a doll. It is unknown if this is Binky Betsy or not.