I just came accross this and I loved it so I decided to share it...
Although there is not a quote in the Bible that states "cleanliness is next to godliness", the Bible is very expressive in several scriptures that He want his people to be clean. He is more concerned about our inward man being clean then the outward. But here's the thing, when your inward man is clean then it produces outward cleanliness. It becomes irritating to live in a filthy state when you
have become cleansed on the inside. There is a scripture in Matthew 23:26 that says, "Thou blind Pharisee, cleanse first that which is within the cup and platter, that the outside of them may be clean also." Jesus was saying what point is it for the cup and platter to be cleaned on the outside while the inside remains dirty. So He said to clean the inside so that the outside may be clean as well. This is proof that He would like for us to be clean internally as well as externally, which means that cleanliness is next to Godliness.
Alexis, O (2011). Cleanliness is Next to Godliness in the Bible | Reference.com Answers. Retrieved April 2, 2014, from http://www.reference.com/motif/society/cleanliness-is-next-to-godliness-in-the-bible.