I can't help but wonder if the concept of the bidet came earlier than the 18th century...Muslims have been using various methods to wash for centuries; it's part of our tradition. For those that cannot afford a bidet - many Muslims by a little pail to use. And now they are creating fancier ones like this: https://www.launchgood.com/project/5_states_50_mosques_500_aquabeans#/
I think they even have travel ones you can use. I remember seeing one before where you can just stick on a small water bottle to use when traveling as well.