I flew to Portland with my bike, rented a one-way uhaul (reserved in advance, 3 miles from airport), threw bikes & luggage in the uhaul, drove to Astoria, returned the Uhaul the next morning. With 2 people, it was very cost effective (cheaper & faster than the bus, cheaper than a one-way rental car) and the more people the cheaper it would be.
I arrived a few hours earlier in the airport than my tour partner, so I just put my bike together, put the luggage on it, and rode to the uhaul place. If you didn't want to do that, it would be a quick cheap cab ride.
My partner had his bike shipped to a hotel where we stayed the first night. They had lots of other bike boxes too. Sorry, can't remember the name.
If I was to do it again, I would just ride to Astoria from Portland, esp. if doing a transam, since you wouldn't be repeating any roads. I used Hwy 30 along the columbia river on the way out of Astoria (on the lewis & clark), and it was just fine. there's a campground/rv park about 30 miles from portland. the portland airport, and portland in general, is quite bike-friendly.