Cost of Taxi to RedHook (ferry terminal) is about $6 to $8 per person (depends on which of the docks you are at). Fro Sub Base this is about a 30 minute cab ride , from Havensight about 10 to 15 minutes. Ferry cost is about $4 or $5. Taxi to a beach on St John another $5 or so. All prices per person. Actual ferry ride is about 10 or 15 minutes at most. Figure an hour total transit time in each direcction.
Maegens Bay is also very nice but can get crowded. Explore the option of Coki Beach or Saphire Beach. Both on St Thomas. While you would still be waiting for ferry to leave for St John, you will be on a beach every bit as nice on St Thomas.