Before Bugs got his house, shortly after he created the carrot peeler, he had a roomy, one-level hole in the ground with just a chair and a lamp. Outside the hole is a mailbox that says "B. Bunny." It only appeared in The Looney Tunes Show once, but it was featured in countless times of the original Looney Tunes shorts that featured Bugs.
The hole's only appearance was in Peel of Fortune, when Bugs got fed up with Daffy, who took over his home, and decided to move back to his little hole in the ground. (After Yosemite Sam suggested he should) He later moved out after it got flooded from rain and Daffy allowed him to move back to his house.