I wanted to make a second bucket nest but I needed something better to line the cut plastic with. There was some cheap duct tape in the barn but it wasn’t enough to prevent a hen hurting herself. That link in the comments a post or two down suggested using a section of tire tube, and that was just the thing.
I replaced some tubes for a neighbor several years ago, when she wandered into some thorns. Took the cast-offs home and they’ve been so useful over the years that I almost regret charging her for the job.
ETA: Some of the Leghorns are using the round bucket, but I won’t be surprised if they refuse the square one. They seem to prefer lower ceilings. It’s kind of an experiment.