Is it better to bleach or dye your hair lighter for a few sessions?

i have a really nice tan and i think lighter hair color is a nice contrast with it. i currently have dark auburn colored hair so its kinda hard to dye it even using the lightest blonde i can find. however i heard bleaching is just horrible for your hair! so im thinking if i should just keep dying my hair blonde for a period of time until i have the shade of brown i want. wich is better?