http://www.seattle.gov/transportation/docs/bikemapsouth6-25-09.pdf
It’s not too bad in the mornings, but it could be a little hectic in the evenings. I’m sure there are others who ride through this way – maybe they will post too.
What I’ve done is use bike route from Lower Bridge, left onto E. Marginal to Hanford. North on 1st and right onto Holgate. Follow Holgate to Airport Way make a left. Follow Airport to Dearborn, the route kind of branches off Dearborn (see purple bit on map) onto the bike trail that ends up on I-90.
You may want to post on the Cascade Bike Club site; you’ll get more responses there from people who do the route regularly and may have really good insight for you. In any case, you should ride the route on a weekend first a couple times to see how it feels for you. It’s not an easy ride.
http://www.cascade.org/Community/forum/index.cfm