I'd always recommend going professional if you want to use bleach. It's so damaging for your hair, especially if you've got hair dye on your hair already.
You would probably need to bleach your hair to lighten it and to cover up any hair dye already on your hair. It will become very brittle and hay-like and could break off at the ends. If your hair is particularly dark now it will more than likely go an orangey colour rather than the blonde you're after, but then you should just use an all over blonde hair dye to even it out.
But definitely seek professional advice first, you don't want to ruin your hair!