Most drivers, and most bicyclists, have no idea what the law is for drivers making a right turn on a street with a bike lane.
Having through traffic overtaking on the right side of a vehicle that is turning right is extraordinarily dangerous. Blind spots make it physically impossible to see the entire length of many vehicles, the turning driver simply can't yield to a vehicle that can't be seen. "Right-hook" crashes are extremely serious. Even Copenhagen, with all its specialized bicycle infrastructure, kills many bicyclists every year because of bicycles passing in the blind spots of trucks.
For that reason, motorists turning right on a street with a bike lane are supposed to merge *into* the bike lane before turning, making sure to yield to any bicycles already within the bike lane. This is supposed to make it obvious that the vehicle is turning, and physically prevent cyclists from putting themselves in the "suicide slot" to the right of the vehicle.
This assumption, that cars will merge into the bike lane before making a right turn, is fundamental to the standard design of bike lanes in the U.S.
Washington law is rather vague on this, using only outdated language from an obsolete UVC. Other states go into more detail, e.g., California code says
"Turning Across Bicycle Lanes
21717. Whenever it is necessary for the driver of a motor vehicle to cross a bicycle lane that is adjacent to his lane of travel to make a turn, the driver shall drive the motor vehicle into the bicycle lane prior to making the turn and shall make the turn pursuant to Section 22100 [general turning regulations]"
The San Francisco Bicycle Coalition has a good infographic for educating motorists to merge into bike lanes before turning, but of course it's annotated with the CVC instead of the RCW.