Lightening Dyed Hair?

My hair is grey. I have been having the hairdresser do light brown for years. Of recent my current hairdresser was using 6 or 7? My hair gradually was getting darker each time she did my color. I asked to lighten it back up and we ended up with black/greenish.

So the same day she tried to correct or get the green out. It has been several months, with a new attempt every 4 weeks or so to undo or gradually get back to light, not black, and it's not happening. We are both hopeful we can process some options and make a decision what to do next. My hair was thick, short, and very easy to manage. The thickness is gone. She is suggesting bleaching. I'm getting other opinions. I would like anyone's feedback. I'm thinking I might just grow it out and be grey for awhile till it gets some length and we can start over. I would appreciate your help. Thanks for any suggestion. I'm most concerned if the thickness can be restored.

By ETG from HI