There was a post earlier this year with some good info:http://www.adventurecycling.org/forums/index.php?topic=8704.0
and there's probably more from the past. Here's my response from this past thread with a little more info specifically catered to your questions/needs.
As aggie mentioned above, you can also take the Wave bus from Portland Union Station (Amtrak) to Tillamook. $10 one way, 2 round-trips weekdays/Saturday, one Sunday.http://www.tillamookbus.com/route-schedules.htm#portland
As for riding to the Coast, I HIGHLY recommend the Hillsboro-Astoria route to the Coast. Hillsboro is a western suburb or Portland that can be reached by MAX light rail. It's a 100 mile ride, low traffic, beautiful scenery!http://www.portlandonline.com/transportation/index.cfm?&a=316549&c=36638http://www.portlandonline.com/transportation/index.cfm?&a=316550&c=36638
So, if you think you'll be getting into Portland at 2pm and won't have the bikes ready until 4pm, you can hop on the MAX (our regional light rail system) from either PDX (Airport) or Union Station (Amtrak and Greyhound across the street) to Hillsboro, the suburb 20 miles west of Portland where this route starts. You don't mention HOW you'll be getting in though. Amtrak or Greyhound is downtown, which means about an hour transit time to Hillsboro. PDX is on the outskirts east of downtown, which would mean more like 1 1/2 to 1 3/4 hours to Hillsboro.
The first camping option is Stub Stewart State Park, 20 miles in. You can make it there in time. Key thing to note about Stub Stewart is there is separated and different walk-in and hike-in campsites. I prefer the hike-in, as they are cheaper and divorced from the main camping loops. You will have to navigate a 1/3 mile of gravel road, and the hike-in sites only have pit toilets and water spigots. (Flush toilets and showers are located in the main loops.) If you have the time and energy, you could push on to Vernonia, another 12 miles down the route. It's not as great of a campground as Stewart, but it makes a shorter day for the next day to the coast. You can also push onto Big Eddy campground, 40 miles in if you want to make the second day even shorter.
After Stub Stewart, it would mean an 80 mile day to the coast which is doable if you start early. There isn't much camping on this route. After Big Eddy, the last "official" campground (40 miles in), there is a horse camping site near Jewell that I've heard cyclists can use, but I don't know for sure.
One thing to keep in mind is services are sparse, so be prepared. There's fast food in downtown Hillsboro and grocery stores in Banks and Vernonia. Smaller stores with limited hours and selection are found in Birkenfeld and Olney. Water can be found in the stores/towns plus at the campsites and at the Elk Wildlife preserve in Jewell.
If'n you wanted other options to the coast, check this page here:http://www.portlandonline.com/transportation/index.cfm?c=36638&a=301633