In '00 I rode the NT between Anacortes and Glacier N.P., leaving around the same time as the year before. In different places in WA I met a group of 2 and a solo cyclist. They were all going in the same direction and only doing parts of the route. In Glacier NP I met another group of 2 that was doing the entire route. The only other riders I encountered in that stretch were on organized tours with Adventire Cycling--the NT and the North Star.
I then reversed from Glacier and made my way to the TA at Missoula and rode it from there to Fairplay, CO, east of Breckenridge. In that short span (about 2 weeks), I can remember encountering 7 groups of two, one group of 3 and 3 solo cyclists riding some or all of the route in both directions, including a Menonite couple on a Bike Friday tandem, an English gent, a couple of Germans and a guy with a prosthetic arm. We rode and/or camped together on a number of occasions.
Amazingly, while riding through Yellowstone, a car pulled up next to me and someone said my name. I looked over and a woman who had been on our NT tour the year before was in the passenger seat. You never know who you might run into out there.