On the bus system from Olympia, you'd have to take a route that goes to Lakewood (I believe 612 is the one). From there, you'd have to utilize other transit systems to get the rest of the way to SeaTac. Intercity Transit doesn't go quite that far.
You would catch the 612 or 620 from lacey or olympia transit center that takes you to 512 park and ride then you would catch the 594 that takes you directly to Seattle. The bus does make a few stops along the way, roughly a 2-3hr bus ride depending on traffic
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