Actually, carbon will not remove chlorine in the way you are describing. Instead of carbon, why not just dechlorinate all the water in the tub at once (with dechlorinator). Once that is done, the water will be ready for use immediately, or as long as a week later (or more). Otherwis, if you let the water sit for 3 days, there will be no more chlorine left. Aging water like this can and will allow for the chlorine to dissapate within a few days.
Hope this helps!