rinsing chlorine from hair after swimming

My hair is usually soft and silky, but chlorine has been building up from swimming, making my hair stiff and brittle. TJs citrus shampoo has usually worked fine once a week, but shampooing even daily after swimming a few weeks has been lathering much less than previously, probably due to the buildup of chlorine. Rinsing with baking soda has apparently removed the chlorine, brought the shampoo back to full lather and removed the stiffness. Thus my plan is to continue with shampooing daily, and use the baking soda rinse twice a week. However, is shampooing this much necessary, and what do you think of the baking soda rinse? I'm interested to see your comments, and how you remove chlorine from your hair.