I didn't grow up in Seattle, but I've been there a handful of times, most recently just last Christmas. The Aurora Bridge doesn't "dump" you downtown, it puts you right on Hwy 99, the Alaksan Way viaduct. That whisks you speedily above downtown, then takes you further south right to the 509 freeway and SeaTac. I thought that was the "secret" route locals used to get to the airport to avoid traffic on the I-5.