This is a rehash of something I posted over on the crazy guy on a bike site, but some of it may be useful. At least some of it is applicable to an Astoria start, but much of it applies to alternate starting points.
We flew into Portland and didn't wind up going to Astoria. We wanted to start our ride on the coast for a day or so. For us the best solution was to rent an SUV big enough for our three bikes. Prices varied widely and not all offered one way rentals, but Enterprise was reasonable. Splitting the cost three ways it was the cheapest option we found.
The bus option was limited in a few ways that made it less than convenient. There was no service to Newport or Florence. We didn't want to start in Astoria, but considered it since there was bus service to there. There were three of us and the buses could only take two bikes per bus. There was no way to be sure we wouldn't be competing with others for the rack space. They ran infrequently enough that riding on different buses didn't seem like a good option.
We wanted to ride a bit of the coast before heading inland so we dropped the car off in Newport, but I am pretty sure there was a place to drop off in Florence.
We rented the car for one day and were able to spend a day sightseeing the Columbia gorge and Portland while we had the car. We rented a yurt at Beverly Beach State Park and dropped the car off in the morning, just within the 24 hour limit.