We have used the Amtak bus from Astoria to PDX and from PDX to Astoria You will probably have to box your bike from PDX, but that should not be a problem if it is already boxed from the flight. When we resumed our Pacific Coast ride last summer in Astoria (we are doing Hwy 101 in three segments: Lund, BC to Astoria; Astoria to Crescent City, CA; and this summer CC to ?) we rode to our local Amtrak station and thanks to a great ticket agent was able to take the amtrak bus from Albany, OR to Astoria. We also lucked out and did not have to box the bikes. We've also used Amtrak for other trips, and found the agents helpful and the bus drivers very accommodating.

If all else fails, the ride over to Astoria from PDX is pretty decent. Enjoy your ride!