I would recommend setting a chair close to the cage when you
wish to interact with it. Just talk calmy to the bird and
see if it will come out on its own, build trust with the
bird, let it know its safe to come out when your around.
Maybe every so often reach in the cage and act like your
adjusting a toy or perch, another way to show it that you
can be trusted and that you're not a danger to it. Maybe try
handing her a piece of food or a treat. If the bird talks,
use words it knows and soothing sounds while your waiting
for it to come out of the cage or when you're moving your
hand around in the cage. Just realize its gonna take some
time for you to gain its trust, and you need to make an
effort to interact with it as often as possible, repetition
is a key tool for alot of animals. Hope this helps, give it
time and I think you'll be happy with the results. Best of
luck to you and your Grey.