No license is required in Washington State when bowfishing. However only non-game species, Carp, is legal and gaffs cannot be used.
Washington State Department of Fish and Wildlife has a great resource for finding fishing areas. You can search by species or county. Take a look at
http://wdfw.wa.gov/fishing/washington/species.htmlAt quick glance I can see about 6 west side lakes that have carp. Just be aware that many west side lakes are in populated areas and I am sure that dead fish floating on the beach will quickly be frowned upon.
As many others have suggested, regardless of what you find in your area, try and plan a trip to the east side. The Tri-Cities is FULL of great bowfishing areas and there is a lot of bank access.
Good luck and hope to see some pictures soon.