Bunny is a Grouch, who has sworn to never show her face on Sesame Street. But, as Oscar's sister, she appears in Episode 4237 as a surprise guest for her mother on Grouchy Mother's Day. Mrs. Grouch gave her the name Bunny just to annoy her.
In April 2011, Oscar answered a couple questions about his sister in the following interview:
Oh yes, I come from a long line of Grouches. I have a sister, her name is Bunny. Mom named her that just to tick her off. She’d rather have had a name like Geezelah or Grumpy, because she is, trust me, a grump.
Do you see her often?