my hair is dark brown, how bad would it damage my hair if i bleached it?

my hair is naturally a lightish mousey brown, but I have dyed it a few times, the most recent being a couple months ago when I dyed it a dark brown with a red tint. It's faded out a lot to where it is more red than brown, but it's still pretty dark. My roots are pretty bad, so it's definitely time I go to the salon again, but I want to do something different. Several people I know have recently dyed their hair blonde, and it's kind of inspiring me. haha, so I was wondering, if I go to the salon to have it done, how much would it damage my hair to go blonde? My hair is long, but not super long, and I would like to keep the length, but I'm afraid that if I dye it blonde, then it would break off and I'd have to cut it short. I don't want it super light blonde, I wanted it a strawberry blonde color. Any help is appreciated, thanks!