We had our car to make our way to the ARC at Gatwick, so I can't tell you if there is a shuttle of any kind right to there (best to call the number as the other person posted) but about waiting, you might want to wait inside the airport, and call them from there to check up on when your animal might be ready for pickup.
We did this; we got off the plane, picked up our luggage from the baggage retrieva area, then went to a cafeteria area next to an information desk. This had all taken about an hour I think already. I asked the information desk if I could call ARC from their phone; I spoke to a woman and said I was calling to see when I might expect to be able to collect my cat, and before I got any further she already said his name! She said they were on his paperwork right now and he should be ready in another hour, then I got directions as to how to get there.
We waited in the cafe area then got ourselves and our luggage onto one of the buses which took us to the long term parking, where my partner went to get the car, brought it to me and loaded us up into it. We had a wrong turn and went around a couple of times before finding ARC (it is not marked at all on the building! But it's right next to the Royal Mail centre).
It was a very small little waiting room with nothing to do, and a family was in there just sitting, which is why I'd recommend waiting in the airport where you can eat and entertain yourselves and even shop, until your animal is ready, not in ARC itself which is tiny and would be very boring to be stuck in, lol. The people were wonderfully friendly though.
Hope this helps.
