I found this link to a map of shore access points for kayaks and boat ramps around Kitsap Peninsula and Bainbridge Island.
https://northkitsaptrails.org/files/WaterTrails_wLinks_LR.pdf
If you try any of these out, let us know what you find.
It looks like there are 3 places in Port Madison. Originally I thought there were none. Then for a few years I knew there was one by Port Madison Yacht Club. This year I heard about the one on the North side of the cove. This map shows there is a third place.
There are 10 places between Keyport and Poulsbo!
Go explore!
Chris.