A more common version of the phrase is, surely, "scream blue murder". The words also appear in phrases such as �get away with blue murder'. The idea comes from French. If something dreadful occurred, the French used to say �Mort Dieu!', meaning �God's death!' Over time, this altered euphemistically to �mortbleu/morbleu' and that translated as �blue death' or �blue murder' in 19th century English. The same use of �bleu' is seen in the French exclamation, �Sacr� bleu!' Nowadays, the phrases mentioned in the opening sentence above just mean �a lot of noise about nothing' and �something terrible'.
I suspect your 'scream bloody murder' is just a variant of 'scream blue murder'.