How do I explain a repair and the bill to a worried homeowner?

You can do the work with your hands; the knot comes when you have to put it into words for someone anxious about their home and their money. That is a different skill, and the fact that you feel their worry means you actually care how they take it. That care is worth keeping. An anxious person mostly needs to feel that someone competent has this handled. So slow down and speak plainly. Say what was wrong, what you did, and what it costs, in plain words, no jargon, no rushing. When you are calm and clear, their anxiety drops, because your steadiness tells them they are in good hands. One step that helps: before you give the number, tell them what they are getting for it. Here's what was going on, here's what I fixed, and that comes to this. People handle a bill far better when they understand what it bought. You already did the hard part with your hands. This is just letting them see it.