While a trim of about two or three inches certainly won't cause your hair any harm if it appears gummy from you bleaching it, it's definitely not something you must do. If you are on the fence about whether to do a trim, then know that a haircut will eliminate the appearance of split ends, thus decreasing frizziness.  Doing away with those damaged strands of hair will restore strands of hair that are less likely to break off and are more manageable.