For more complex changes in colour, I would always recommend to go to a stylist that is specialized in colour (in The Netherlands you can go to tony&guy for such a specialist, but I'm not shure what it is like in your country). It will cost more, defenitely, but most 'usual' hairdressers are, in my experience, not capable of colouring hair that is already coloured.

I think there are different options for you:
1. growing the dyed hair out. Yes, it might look silly, but you keep the new hair healthy and you will not furhter damage the already bleached hair
2. go on with highlighting, but everytime have less of them, untill you don't have them anymore (speak with your stylist to make a plan about this)
3. add lowlights to your highlighted hair

but again, I'm not a stylist. But there is one thing I can defenitely not reccomend: trying to colour the bleached highlights in your own colour. It's so difficult to do that, it's almost 99% shure it will fail. And bleached hair can turn green when it's coloured darker again.
highlighted 3a hair. Fine strands, medium to high density. Probably high porosity. Growing uit bad layering and aiming for waist lenght!

Pre-poo: coconut oil
wash: CJ Daily fix or SheaMoisture Coconut&Hibiscus
RO + LI: different every time
Styler: CJ Pattern Pusha, CJ CIAB

dislikes: glycerin in low dews, scissor happy stylists, magnesium sulfate

(modified) CG since june 25, 2012
Hiarfinity + extra MSM since March 5., 2014

SL - APL - BSBL- BSL - MBL - WL (stretched)