You might want to check out our sister site Port Reviews, there is very specific information about King's Wharf: http://www.bermudaportreviews.com/KingsWharf.htm
I have been there often and just returned a couple of week's ago from a cruise on the Costa Magica. There is a beach at King's Wharf but it is definitely not the soft pink sand beach we equate with Bermuda, but a rocky beach good for snorkeling. King's Wharf is on the very eastern tip of the island and the best way to get to the other parts of the island is to take one of the regularly scheduled ferries or buses. You can purchase a 1 day pass for $12 or a 3 day pass for $28. The pass allows unlimited use of all ferries and buses and is a great bargain compared to taxi fares.