I have brushed my teeth with pure baking soda for years, never did the Clorox part.
You are way ahead of the game. . . and saved all that money on Toothpaste which our main dentist calls handy-dandy sweetened pumice! LOL! The purpose of the Clorox protocol is to get the last few bacteria (spirochetes) that are too tough to be killed by the baking soda protocol. Baking Soda has a five second kill time which may be long enough to allow some of the spirochetes to ball up into what is called the "spore" form. The sodium hypochlorite of the dilute Clorox Dakin's solution has a two second kill time, far too fast for the spirochetes to for their protective ball spore form. . . and even the toughest will be killed. We don't want to breed generation after generation of tough spirochetes!