I camp at a private camping club from time to time. It is family oriented and there is a no alcohol rule. Nearly everyone there has a few beers over the weekend but you never see it. We have three rules:
1. Pour the beer into a regular plastic drinking cup.
2. Don't let your empties out of the camper.
3. Limit the number of beers you drink. If this one is difficult take only a few with you to avoid the temptation.
There are a few club members who strictly enforce the rule and go as far as checking the trash after the weekend to look for evidence but we avoid that trouble by taking our empties with us.
I can't speak for the Bristol Campsite but it is probably like anywhere else, if they don't know it's there they can't say anything.
Lou, Becky & Children Lizzy & James
AA3LJ & N3SEE