The concept of "Bed and Breakfast" on the west coast is different from the rest of the world. Out here, B&B is sort of a fancy hotel, where they fix you fresh muffins in the morning. In Washington, B&Bs are considered businesses, so the usual red tape applies. That jacks up the price.
However, you can access some B&Bs in Seattle at www.seattlebedandbreakfast.com
And, don't forget that Bainbridge Island is only a 30 minute ferry ride from downtown Seattle. I usually stay at the Island Country Inn on Bainbridge. There is a website for other lodging at www.BainbridgeLodging.com.
There isn't any lodging withing easy walking distance of the ferry dock, but motorcyclists generally park for free along the fence at the East end of the parking lot. Then you could walk the waterfront in Seattle, or take the free downtown busses.