Premier Inn does do transfers-we used last year. Did twilight check-in, went down to bus area, they have a board that shows all the hotels and which bus-stop to stand at. I think Premier Inn's buses were every 20 mins-we didn't wait long. Only on bus 5 mins, plenty of room. Hotel confirmed bus times for next morning. All went very smoothly. Nice clean rooms (not very big but that wasn't a problem for one night), Quick check-in/check-out procedure, nice bar-meal in the evening, good breakfast buffet etc.
We've used several 'Gatwick Hotels' this was by far the best (apart from those at Gatwick-Hilton etc, but half the price of that!) & one of the cheapest