I don’t know about the annual pass but to get the 13 dollar senior rate you need to purchase a senior national park pass. The cost is 80.00 for a lifetime pass or 20 for a yearly. Here is a summary and website to purchase.

There is a self-registration fee of $26.00 per overnight for anchoring or mooring between the hours of 5:00 p.m. and 7:00 a.m. Golden Age/Access Passport holders pay half price. Overnight fees must be paid prior to spending the night. Overnight stays in the Park waters are limited to 30 nights in a particular calendar year, and no more than seven consecutive nights in one bay. Payments are deposited in an envelope (found at this station) within this floating pay station. Floating Fee Stations are found at Leinster Bay, Francis Bay and Caneel Bay. Land-based fee stations are found Cruz Bay Visitor Center (near the flag pole), Salt Pond Beach and on the VIERS dock in Lameshur Bay.

https://www.nps.gov/planyourvisit/passes.htm