New Betta! Minor Fin Rot

I just picked up this betta from a local Petco. I was won over by his colors and overall health, and mild temper. He is in my 7g bookshelf with a school of pygmy cories and wild type shrimp. Originally my plakat was going to go into that tank, but after about 30 minutes of constantly harassing the cories he's back in his 5g tall. I'm really happy with this guy, but I'm concerned about his fin rot. It didn't seem that bad at the store (next to every other half-dead fish, of course) but I want it taken care of. What would you recommend I do to treat this? I'm hoping that if I just give him the opportunity to have a clean, stimulating environment he'll be able to fight the infection off himself. I can keep him in a 2.5g bare-bottom tank to treat with aquarium salt if I have to.