Actually that sounds a little more like gill hyperplasia caused by the ammonia poisoning...
Here's a link explaining it. http://nippyfish.net/sick-betta/gill-hyperplasia/
Fortunately for you, treatment is roughly the same, but will probably take longer. While they're sick you need to do full water changes every day, with a little aq. salt and the conditioner. You shouldn't use the aq. salt for more than ten days, or you risk doing even more damage to them.
Its generally 1-2 tsp/gallon, so in your case I'd start by disolving 1/4 tsp in a bowl of the bowl's water and then pouring that in, then gradually increasing to 1/2 tsp. As for how long to wait before you put the fish back in, keep it in a little plastic baggy with the old water (submerged in the tank, you might have to use something to keep it hooked there since you don't have a lid to help), then filling up with the new water a little at a time over the course of at least an hour before putting him back in.
I do suggest at least upgrading to a 1 gallon bowl in the future, but if for some reason you absolutely CANNOT, don't feel too too bad about it, mine's had to stay in a half gallon bowl since I got him a few weeks ago while his bigger tank cycles, he's been pretty healthy with daily water changes and SeaChem's Prime as a conditioner. But you do have to keep up with the water changes in a bowl that small (like someone else said, at least every other day), the water gets pretty bad pretty fast. Its a pretty time consuming process, but with a tank 2.5 gallons or bigger, you only have to do partial water changes a few times a week ( = one very very good arguement for switching