One of my favorite bike rides while living in Bremerton was out of Port Orchard. We would ride along Puget Sound thru Manchester to the Ferry Port in Southward.
We could take the small boat from Bremerton to Port Orchard but it was easier to park in PO. We would often pass cycling clubs from Seattle that would take the ferry over and ride to Bremerton and return by ferry.
It was fun to watch the clams spitting water when the tide was out. People would wave as we rode by.
Manchester State Park looks like a great place to camp. We would stop there sometimes just to wander. The mornings can be chilly but dress warm.