Hello Heidi,
Your over bleached hair does need a rest for several months, however once you have a root of one and a half to two inches, a professional and competent hairdresser could tint your roots only to take away the grey, they should choose the closest colour shade to the hair colour it is now. That way at least during your growing out time you don’t have to walk around with grey roots.
Your hair will grow around one centimetre during each month. Depending on the length of your hair you should be able to work out yourself how long it will take to grow the damaged hair out. Cutting the hair shorter would help to speed up the waiting period, as soon as your hair is back in a shiny healthy condition a professional salon can start fresh in providing the colour of your choice.
Hope this helps!