I don't watch the show, but I read the novel. Dexter is a serial killer who hunts down and kills other killers. He was adopted by a law enforcement agent who recognized his murderous tendencies when he was a young boy, and helped Dexter to channel those "desires" to do good.
He is very thorough in his clean up. He uses plastic sheeting and gloves, etc. he very thoroughly disposes of the bodies which are never found. I think he may be a detective by day, so he can get inside the cases. (May be misremembering that part) Dexter keeps a microscope slide with a drop of blood on it from every one of his victims as a trophy.
I'll see if I can find the book, and I'll check if bleach specifically is used, but I think in general, the answer to your question is yes, Dexter gets away with it by not leaving trace evidence.