I went coast to coast on the mid trans am route going east to west in may of 1999. I was off the route for about 1/3 of the way.
I met a great pair on a tandem in Missouri and didn't say goodbye to them until reaching the Grand Tetons where they went around the other side to avoid Yellowstone.
While I was on the route I met many riders. At one point in Kansas there were 10 of us camped in the city park. 5 going east and 5 going west. 8 of us went out to dinner together. Three were a couple of people in hotels that night too.
I saw people almost everyday while on the route. Towards the end you don't want to stop and talk to them anymore. I saw 9 people in Yellowstone in one day. All were on long rides.
Many towns welcome bicyclists. Its good to check in with the police in some of the small towns in Kansas just to let them know your going to be in the park camping. Sometimes they will open bathrooms for you. Cyclists represent important business for most of the small towns. I had some great experiences.
Read my journals at http://www.ericactive.com
Feel free to email me with any questions.