Bremerton is located on a peninsula across Puget Sound (from Seattle). Washington State operates ferries from Downtown Seattle to Bainbridge Island and Bremerton. You can walk/bike or drive on (recommend getting an advance reservation if driving). The ferry to Bremerton should take about an hour or so.

There is a substantial amount of commuter traffic back and forth, so the schedule is fairly regular.
https://wsdot.com/ferries/schedule/s...roundtrip=true