Hairdresser disaster in purple

So, let me introduce you to my dilemma:

1) 2 months ago, I went to the hairdresser, she bleached my hair. With 40 vol. Came out WRONG. Totally dark instead of blonde, on my virgin black hair. Virgin, not dyed not nothing. And I've used box bleach and managed to get to blonde before so this, with a 40 vol. is unacceptable.

2) Put Directions Plum over the mess. Came out quite purple because it's forgiving and the hair didn't look that bad.

3) Now that's faded, I'm stuck with this situation (see pictures attached). The greenish / orange parts are the ones that were barely bleached. Another hairdresser told me the hair "looked saturated and that I shouldn't bleach over that again", she told me the hairdresser did something wrong or something and that's why a 40 vol. bleach didn't lift my hair.

So what I'm asking is if I should bleach my whole hair before I dye over it again, or should I just bleach roots and keep dying purple over it and let that mess aside. I bleached my hair 2 months ago, haven't bleached it since.
I honestly don't know why she couldn't do a simple task like bleaching virgin hair. I'm never trusting hairdressers again. Never.

Thanks for your help and suggestions in advance.