Hydrogen peroxide is cool because it's instability is so useful- cleaning wounds, cleaning stains, bleaching, rocket fuel, yep- rocket fuel
At the rate of dilution that the average citizen can purchase HP, it usually isn't going to remove much color. When baking soda is added it becomes a little more unstable, and releases the oxygen from solution quicker than without the soda. That release is what does the job of breaking down stains and odor. After about 5 minutes the solution is nearly inert with increased salinity.
Don't try this with table salt. HP releases Idoine from the solution and the stain is nearly permanent.
HP and chlorine is really really unstable. Don't even attempt it. Goddard and Von Braun had fun with the stuff.
So much for high-school chem. Tune in next week when my eyebrows have grown back. 😉
Bob H