Hi, Chris. i am pretty certain that the car park near Whittlebury is one of the designated car parks. if you get there early enough you can park very near one of the entrances. i am not sure how you gain access to that part i have only ever gone out that way. You do not access via the golf club though i am pretty sure of that. All the years i have been going i have never seen a shuttle bus. Best thing to do is give Silverstone a ring and explain your situation, they are normally very helpful.
All the best, have a great day/ 3 days