The Bremerton-Kitsap Airporter provides shuttle service from various locations around Kitsap to the Seattle airport, and vice versa. You can purchase reservations online. The stop closest to the wedding venue is Silverdale Beach Hotel. To board at the airport, follow signs for shuttle service and locate the Airporter waiting area outside.
Kitsap Transit has two ferries available from Seattle to the Peninsula: one arriving in Bremerton and one arriving in Southworth. Bremerton will land you closer to the wedding venue. Board the fast ferry on the lower level of the ferry terminal in Seattle.
Washington DOT has "slow" ferries from Seattle to Bremerton whose crossing time is about 1 hour. Unlike the Kitsap Transit fast ferries, these ferries can accommodate a car, so you could rent a car at the airport and then drive it on to the ferry!
Best Western Plus Silverdale Beach Hotel is about 10 miles away from Scenic Beach State Park. It is located on Dyes Inlet, so you can enjoy a water view during your stay!
Baymont by Wyndham Bremerton is about 14 miles away from Scenic Beach State Park. It is located near several parks, as well as Kitsap Lake.