Our rubber-backed bath mat is falling apart, mostly because I have to wash it a few times a week as the family dachshund uses it for potty when nobody notices she needs outside. Or when it's raining and she doesn't even try to tell anyone. I am not loving the rubber backed type rugs anyway, because they smell bad when wet, and take a long time to dry!
Amanda has this project in her book to use a towel that is no longer being used, and some fabric--perhaps sheets that aren't used anymore either. I took advantage of the possibility that I'd find something at our church thrift sale, and I found a towel bath mat (the size of a bath mat, but made out of the loopy towel material), and a really cool print on cotton, but thicker than quilting fabric.
The mat cost $.50, and the fabric $1. Not bad! And no more yucky rubber smell.