If you are having a breakage issues, bleaching your hair is only going to add to the problem. You should never chemically process hair that is breaking & splitting on its own.
Maybe you aren't handling your hair gently enough? Maybe you need to try new products?
You mentioned that the winter has been dry, & from your hair regimen, I don't see any moisturizers listed. I see conditioner, but I know that conditioner only isn't enough for my hair. You might be having the same problem. My advice is to find a good moisturizer. Maybe you can try the baggy method to see if it helps you out. I know some of the ladies can recommend good moisturizers. I'm not CG, so I never really do product recommendations.