Bleached out red dye from hair and it turned yellow orange, do i need to bleach again?

I went to the salon a few weeks ago and asked for pink hair. I have natural dark brown hair which they bleached twice and then dyed. Problem is it turned out bright orange. I went back to have them correct it. They bleached out the red hair dye this time and it turned yellow with some light orange. I want to get rid of this brassy color and have it turn whitish or the lightest yellow so I can dye it pastel pink. Should I bleach it again? I'm concerned about the damage it might do to my hair.