If you use water conditioner you don't have to wait 24 hours. You can add water in right away. Since you keep him in small bowl now, I'm assuming it's not heated, so you may want to keep him somewhere where is stable temperature and away from the window. Bettas do heal better if they are not cold. You can keep light off, daylight should be enough for few days. My bettas don't have any artificial lights, I keep them on the bright spot in the house, but away from sunlight.
You also mentioned you have well water. I was just wondering if there may be some small organisms that cause problems in digestive system. Some bettas are stronger than others, so it's really hard to say without proper water analysis.