Dave.
I talked to a nice lady in Bainbridge. Here is what I found out.
Anchoring in WA State is allowed, where there are no restrictions, for 30 days. After that, you need to move, but you can anchor another area for another 30 days. That's it, 60 days total a year for free anchoring.
If you want to moor on a buoy at Bainbridge, you can do so all year long for a fee. It is calculated based on the boat's length depending, if you are with one, or two buoys connected aft and bow. The minimum charge is $175. This is for a 30' boat. Anything above that is $1.50/foot. So, if you have a 50' boat, you will pay 175+30=205 dollars per month. For this, you will get nothing, except the spot on the water. No parking, no shower, no power, no water. You can dinghy out and leave it on shore for free, but everything else is up to you. The ferry is less than a mile away, so walking there can be managed. The ferry ride is 35 minutes to downtown Seattle and the monthly pass is $105.
There is an application form for mooring on buoy. You can download it from here:
Documents, Forms & Applications | Bainbridge Island, WA - Official Website
The form has the foot/charge calculation info at the bottom. It has to be submitted in November, each year, and the process takes a month. By the end of December, you will know, if you have a buoy to hook up to, or not. The contract is for one year commitment. The City decides, if there is a free buoy, or not. It is possible that there will be nothing available and you need to try it again a year later.
There are also about 500 privately owned buoys in the same area. These belong to citizens and you need to contact them directly. The City is not involved with those, as long proper permits are obtained for the buoys.
If you choose marina mooring, with water/electricity/etc. you will pay $12/foot/mo. Not much cheaper than Lake Union, or even more in some cases. Bainbridge is a beautiful place, but unless you live and work on the island, it is not the best deal.