Google maps says it is 2km to the north end of the 'high street' and 2.5km to the southern end (roundabout by the banks) - both by the bottom of the airport route.
We have always walked to and from Arnage from Parking Bleu. Pleasant walk down the lane. Remember to say hello to the bad tempered donkey in the field on the LHS.
As above, walk. saves all sorts of problems, and as I understand, the lane out is closed to traffic on race day, so a safe stagger back - just mind out for the ditches
I've walked to Arnage from BN for some food at some point during the weekend for the past 6/7 years. It seemed a lot further back then than it does now.