LYD,
I agree with AdoniP about the Premier Inn (same bus numbers, but you might have to pay as its further out). I was there last week on a course and aircraft pass VERY, VERY close on approach.
HOWEVER, as DaveR mentioned, if aircraft are not landing on 27R, its a waste of time being there, because you can't see the runway at all. You'd then have to get the bus back to the Academy. Also, I know you have already mentioned that you are using the bus, but be aware, that it is difficult to get into the car park through the barrier unless you are a legitimate guest. Walking through the barrier, is of course, no problem.