I don't want to go down to Astoria but want to get on (connect) to the TransAm route as quickly as possible starting from Bellingham.
If you're looking at expediency, I would look at some variation of the RSVP/STP/Willamette Bikeway option. This would take you along the I-5 corridor for the most part, and be fairly (but by no means wholly) flattish.
The RSVP route (Vancouver BC to Seattle) is an annual ride put on by the Cascade Bike Club. Map and cue sheets here:http://shop.cascade.org/sites/default/files/RSVP-Route-Map-2011.pdf
STP is the annual Seattle-To-Portland ride, also put on by the Cascade Bike Club.http://shop.cascade.org/sites/default/files/STP-Route-Map-2011_web.pdf
That'll get you into Portland. From there, you can use this routing to get to Champoeg State Park, the start of the Willamette Valley Scenic Bikeway:http://shop.cascade.org/sites/default/files/STP-Route-Map-2011_web.pdf
And from Champoeg, ride to Eugene to connect to the Trans-Am via the WVSB:http://www.oregon.gov/OPRD/PARKS/BIKE/WVSB_main.shtml
A few notes about all of the above: It will still take you about a week to get from Bellingham to Eugene (still don't know what the mileage per day you are aiming for.) You won't get to see the actual ocean on this route but you'll see some of Puget Sound between Tacoma and Bellingham. Some of the route is fairly meandering, so there are ways to straighten things out a bit, or detour off the route for more scenery (like Whidbey and Vashon Islands.) But all of the different routes above are well mapped, whereas detours not so much.