Can I still bleach my hair when it's already dyed?

I'm actually a brunette and I want to achieve this Carrie Underwood like blond, but then they advised me to dye my hair 3x with golden blond dye, so I did and turned reddish brown, so it's now half-dry, and will be using a hair spa to bring back the softness and they said I could still bleach it, and so... what am I gonna' do now? Help...