Flat Battery

Advice please.
went out to go to work this morning, and the battery was
almost dead, the central locking barely opened the locks.
Luckily I was on a hill so bump started.
Half and hour drive to work, and there is a charge in the
battery now, dash lights bright again etc. The condition
window on the battery is black (requires recharge).

Is the battery finished, or can it be topped up with
sterile water to bring back to life.
Is it worth contacting the AA to let them test it?

Andrew,
thats weird the label on the battery definitely says if
black it has insufficient charge, yellow replace battery.
Oddly its been fine since then, but I have been careful
with heating blowers and air-con.
Will be going for a short journey tonight with lights on,
will see what happens in the morning.

There is actually some useful info on this within the
sticky for 5-series, which tells you how to top up with
battery fluid, may give this a try at the weekend.
Pete