If you are concernd that your Betta has fin rot....Dont panic! :] Just change the water everyday for the next week. This will provied a healthy habitat for your Betta and its growing process! Also, what are you feeding???
And the 1 gallon is fine for him as I have all my males in 1 gallon vaces...But you dont want to have any decor. in the bowl/vace. Try finding a plant and letting the roots hang inside the vace/bowl and let the plant grow out from inside the vace/bowl.
This has worked for me many many years...