About 10 years ago, I picked up a book of scifi stories off my lab's bookshelf and read a few of the stories. One of these was set in a a post-semi-fall-of-society-world, where the Church was heavily persecuted. I don't remember much about the actual plot, except that a priest or religious had been sent to check out a holy hermit living in the hills to find out if he was the real deal or not. I remember the priest, having to hide the fact that he was a priest, would wear a jacket or other garment with buttons to use for praying the rosary. I remember he rode a robass. I personally did not have trouble figuring out what this meant, but a helpful previous reader had scribbled out the formula "robot + ass = robass" in the margin. Actually, that equation, and it's family of spin-offs, is probably the reason why I remember this story at all still today.
The story you desire is "The Quest for Saint Aquin" by Anthony Boucher, first published in 1951. You may have read it in The Science Fiction Hall of Fame, Volume One. I confess I haven't read it myself, though I've read many other titles in that collection. Here's the story's Wikipedia page and its Technovelgy page describing the robass.
...I think the "big twist" is that the hermit is an android who calls himself St. Something-Or-Other, but of course he doesn't know he's an android, and the priest is left with the decision of what to do. The old, is it better to give people hope, or what's the harm type of fingernail biting. The best I can remember, the title of the story was something like, "Looking for St. Something-Or-Other".... I read it in 1999 or 2000, but I'm guessing the book was not new at all at that point.