Yes, it is possible to have soft bleached hair. Bleaching can damage the hair, but by taking proper care of it both during and after the bleaching process, you can help keep it soft and silky. This includes preparing your hair before, using a deep conditioning treatment after bleaching, and avoiding harsh styling products. It would help if you also were sure to use sulfate-free shampoo and conditioner and consider using a silk or satin pillowcase to help protect your hair at night. With the proper care and attention, you can keep your bleached hair looking and feeling soft and healthy.