Christmas at Plum Creek
During the Ingalls first Christmas at Plum Creek, Laura traded Bunny for a stove for Caroline. Laura is shown to have a strong relationship with the horse. She however has ideas for trading Bunny when she sees Caroline admiring a stove at Oleson's Mercantile, with a high price. Laura eventually got to talk to Nels Oleson about the deal and told him to keep it a secret. Him keeping it a secret caused Charles to order another stove for his wife though. In the end, Caroline gets her stove, and Bunny is sold to the Olesons.
Years later, Bunny is returned to Laura when Nellie handles Bunny too roughly, she goes wild and throws her off. She is not seriously injured, but pretends to be paralyzed. Harriet demands that Bunny is shot because of this. Laura then takes Bunny back to the Ingalls. Out of guilt, she wants to help Nellie by bringing her homework to her house, (and doing some of it). Laura one day sees Nellie walking around and decides to expose this by rolling her in her wheelchair into the pond. Nels then gives Laura back her horse. (Episode 116: Christmas at Plum Creek)
Laura and Nellie go against each other in a horse race. Harriet buys Nellie an expensive thoroughbred to go against Bunny and Laura in a race. But when Willie Oleson is in need of Doctor Baker, Laura rushes to get him on Bunny. (He was leaving the town.) It turns out that Willie just had a bad stomach ache from eating too many candy apples, but Bunny is too tired from getting the doctor to do the race! (Episode 304: The Race)
When Laura's grandfather is staying at the Ingalls, Laura was showing him how well she could ride him when she trips over a wire fence. Bunny is badly wounded and Charles is forced to end her suffering and pain. The horse's death left Laura very sad and angry that she scorned her grandfather for a time. (Episode 307: Journey in the Spring (Part 2))