It is not illegal to bicycle under the influence in Washington State.
If an officer pulled you over for bicycling under the influence, the officer might take you into protective custody (meaning take you and your bicycle to a safe place, or release you to a sober friend).
There are many reasons why you would not want to bicycle drunk, and the officer could give you a traffic ticket for violating the rules of the road, but a bicycling under the influence charge is not one of them.
This is a general discussion of legal principles by a Washington lawyer and does not create an attorney/client relationship.
You cannot be charged with Bicycling Under the Influence in Washington State, it is not (yet) a crime. The reason is that the bicycle is not a motorized vehicle as defined by statute. Arguably, if you chose to ride your bike rather than drive after drinking you should be applauded. Personally, I would take a cab!