To keep the low-maintenance whilst working away, the best way to blend the colour out while growing it out is to go all natural. You would do this by doing fine, natural scattered highlights throughout the hair.
This would blend out any regrowth line created by existing colour and give a more natural look. The highlights will give a less harsh line and look more natural, making it easier for you to leave it and not worry.
The colour choices I would choose is a colour closest to your natural hair colour as possible, also some pre-lightener, and then tone to a silver/grey (12/81 or 12/89 depending which is closest to your regrowth colour). The amount of each colour ratio I would use would depend on the amount of grey you naturally have (the more grey you have naturally the more grey highlights, if your majority is more naturally dark the more dark highlights I would do). The idea would be to get your hair looking as much like your regrowth colour as possible.
Technical spec for pre-lightener:
Bleach with 20vol (6%) and tone using 10vol (3%)
Natural dark tone closest to natural colour, use 20 vol (6%) to make sure you get coverage on white hair.
Ashley Gamble, Ashley Gamble, Shifnal