When I did my NT I used Bikeflights to ship the bike to Anacortes. This made the flight and the bus trip far less stressful. The bus dropped me off within walking distance of my motel and the bike shop so it was very easy to get organized. I'd recommend you chose a bike shop that is close to transportation and a motel and once you are set up just ride to the trail head, be that 10 or even 100 miles.
I’ve done something very similar for my tours out of Missoula. Shipped to REI, which is literally around the block from the KOA. Land, taxi 3 miles from the airport, check into the KOA and walk around the corner to pick up the bike, which is built up and waiting for me. No fuss. No muss.
When I twice started in Seattle and went north to pick up the NT at Mount Vernon I took Amtrak with the bike, stayed at the Seattle HI and rode a couple of days up to the route.