Greyline Bus goes from SeaTac to the pier. But with all those people you are going to have to pay per person and its about 27.00RT PP. I think you are going to be better off using a shuttle service like Super Shuttle. Or even 2 Taxis would cost less then Greyline.
I did a little research for you and found there is a company called Shuttle Express that charges 72.00 each way for up to 10 people in a private van. The phone number is 425-981-7000. This is the web address: http://hudsonltd4.com/cgi-bin/sea1/res
If you can handle your own bags and like to save $$ like me for the next trip, I suggest taking the Metro city bus #194 that runs every 20 minutes from the airport to Seattles Chinatown. Get a transfer and walk across the street to the Waterfront Steatcar that also runs every 20 minutes direct to Pier 66 where Celebrity and NCL sail. Fare $1.25. If you'''re sail on Princess or HAL they sail from pier 30 out in the freight docks with no public transit. You will need 3 cabs for your gang @ about $25 to $30 each from the airport.