A bowl is actually fine for a betta. They're designed to live in still water, that's what the labyrinth system in their gills is for that lets them breathe surface air. The problem with a small enclosure is water chemistry, as you have just found out. In a larger tank/bowl/enclosure of choice, the water chemistry is much more stable.

Hard to say if he'll recover or not. It depends on how extensive the damage was. Just keep doing what you're doing is really the only treatment at this point.

And if you're referring to my comment, I wasn't trying to troll. I just think that no matter what animal you have, whether it's a $5 fish or a $5000 dog, you should know what the best way to care for it is and do that, or don't get the pet. How much the pet did or didn't cost is irrelevant.