Hello fellow passengers....just wanted to give you all a warning regarding a shuttle service from seattle airport to the port....called graylineseattle. The service schedule on the internet is very misleading. The staff has no idea of this internet posted schedule. I called to confirm the schedule and staff members had no idea. Also the manager was very rude to me. I asked her if she had seen the schedule and her reply was "no"...when I tried to explain why it was so confusing she was just rude, sarcastic, disrespectful. I still did not get a clear answer on the service. They will not refund our money either...so we MIGHT have a shuttle...if not we will end up paying again for transportation and lose our money in the process. Don't make the same mistake we did.
I used graylineseattle last September. I also booked online and likewise, noted the schedule provided. I'd like to convey a bit of what I experienced to ease your anxieties (or not). Don't assume that Gray Line coaches will follow posted schedule/timetable. What they do is process passenger loads to best of their ability--schedules adjusted according to the amount of passengers they have to deal with. During peak times there are lines of passengers and street traffic to deal with.
After you collect your luggage(baggage claim area), walk out the doors at street level, turn right and walk to the booth to exchange e-confirmation for boarding tickets. Then walk just a little further down (likely will be a line of people & luggage) to wait to board a bus. If you don't see a Gray Line coach just be patient for the next one to arrive. The bus drivers are usually female and have to manage much luggage and passengers. Eventually, the bus gets loaded. You and fellow passengers are then dropped off at various locations and selected hotels. Heavy traffic can slow the whole process down. The driver on the bus I rode was very chatty and friendly with the passengers. She tried to ease travelers' frustrations a bit by giving us info on Seattle itself and joked around with some of the passengers. Seemed like everyone relaxed a bit and forgot their troubles.
This particular service is best utilized by those who are arriving SeaTac a day or two before the cruise departure date. As you mentioned, they are not as organized nor do they hold to posted time table. Be patient and have some flexibility....and graylineseattle will get you to your drop off point.
I arrived in Seattle at 11AM and was at the front desk of my hotel by l:00 PM.