It is a public beach, as I believe all the beaches in Antigua are.
The beach has a curve to it and I know it has two hotels on it, along with just open areas and the locals selling their wears. They are not obtrusive and are friendly. I know there are two places that sell food and drinks.
You can catch a cab right at the ship's terminal and go along with other people from the ship as soon as a group is formed. The beach is not really crowded.
To get a look at the beach look up
www.longbayhotel.com If I wasn't on a cruise this is where I would be.