It is my understanding that the likelihood of seeing The Orca Whales is better during the summer however you can still see them during November as well as other different species of whales.  I recommend you listen to this interview to get a good idea of what to expect... just click on the below link and scroll down to watch the YouTube videos.  The video is an interview with a whale watching company on Orcas Island that it is offering tours year-round. Whale watching interview video .

Transportation options:

Kenmore air has daily flights from SeaTac and Lake Union to the San Juan Islands.  Ask them about the likelihood of fog during November before booking.

Here is a shuttle service from downtown Seattle to the ferry landing in Anacortes.
current schedule
homepage

Here Is another shuttle service that departs from the SeaTac Airport which is about 45 minutes south of Seattle.  This is less convenient however it is an option. http://www.islandairporter.com/

The other option would be to rent a car.  This might be a good idea because you will have total control over where you need to go.  With such a limited amount of time I think this is the best option.  Rent a car in Seattle, drive to the Anacortes ferry landing, and drive on the ferry and drive off on Orcas Island, drive to your hotel or bed and breakfast, then start exploring all of the Places on Orcas Island . Here is the ferry schedule .

Enjoy your trip and thank you for posting on the message board!