I had a betta at the LFS that lost nearly ALL it's fins to aggressive tank mates. I moved him to a tank with only ember tetras, added some NovAqua+ and did extra water changes.
After about a month he had grown some fin back and could get around better, we called him "Bob", which was about all he did for another few weeks. After about 3 months he looked and swam normal but I think his fins were still growing in as they seemed slightly short.
We had others with injuries at times but Bob was the most severe and his treatment was just clean water and time.
Actually, I can't remember ever treating any of the bettas for fin damage, most healed up in about 2 weeks with good water.
I've never treated with or regularly used aquarium salt.