While both the chlorine used in pools and BS are alkaline, it is always a bad idea to mix any chemical with chlorine. BS won't create mustard gas like some other chemicals would, but other noxious fumes could be created. Not to mention that the mixture will raise the pH of the water. You want the pH on your scalp to stay constant. water is usually slightly over 7. Raising it makes your scalp too basic. It won't burn like an acid, but it can cause mild chemical burns if you don't rinse it out really well and right away. It's just not a good idea.
I couldn't tell you the concentration of BS you could use safely without knowing the concentration of chlorine in the water.