Yeah, as AT mentioned in his post, there is a lay by exactly at the foot of the bridge, in the circumstance that there are no spaces, just park up on the other side of the foot bridge - the side parallel to the train line!
I have never had any trouble whatsoever at the footbridge with the public or anything for that matter, a lot of people do tend to stop and look over into the airfield in hope that they might just see aircraft movement, but yes, almost certainly, do keep your wits about you, but I cant see there being much trouble!
Jake