If you treat him in anything less than a 10 gallon you will most likely overdose, which can kill the fish. You *will* overdose in a half gallon; measuring things out correctly for such little water is near impossible. Fish with fin rot also need very clean water, so the more fresh water available, the better. Keeping your betta in a half-gallon bowl for treatment will probably worsen his condition.
Malachite green is primarily for parasitic infections, not fin rot (though it can help with fungus, but not bacterial). It sounds like your betta has a bacterial infection, treating with malachite will most likely do nothing but stress your fish further.
When it comes to owning animals, anything that contributes to the animal's good health is cost effective. If I were you I would have gone with the Bettafix. Bettafix is Melafix, just with smaller more accurate dosage instructions for betta bowls. Many people say Melafix isn't good stuff, but I've used it periodically for years and have seen great results.
You really need to consider getting a larger treatment tank, though.