From Seattle you need to get to Everett Station - by Community Transit or Sound Transit
From Everett, you can take Skagit Transit to Mount Vernon Station. The bus is called the _Everett Express_.
From Mount Vernon Station you can take the county connector bus 411W to March_s Point Park and Ride.
From March_s point Park and Ride you can get on the Skagit Transit route 410 into Anacortes.
Bus schedules:
Skagit Transit:
http://skat.baron-co.com/index.cfm?pageI��
Sound Transit: www.soundtransit.org
Wish I could help more, but perhaps that will get you started, at least. Good luck!