It might be easier now that Oktoberfest is over. I would still plan ahead somewhat. When I did the Katy Trail last October, I camped most nights and stayed night in a B&B Hartsburg and in a RV cabin in St. Charles. I called and made reservations. When I spoke with the people running the different locations, I explained to them I was doing my first tour and I was traveling alone, so while I had an itinerary, I wasn't sure if I would hit the exact days. Most places said they could be flexible and could accommodate me if I was a day or so late. They asked that I call ahead if possible, especially if I was not going to stay at all. The places that couldn't accomodate me were already booked.
Check out www.bikekatytrail.com. It has links to towns and tells you what is available in the terms of lodging and other fun stuff. My trip, which started in Clinton, and had overnights in Sedalia, New Franklin, Hartsburg, Blufton, Marthasville and St. Charles. I took Amtrak back to Kansas City, which required a $10 ticket for the bike.
Performance mountain bike, Giant Cypress LX hybrid, Surly Long Haul Trucker
I camp when riding the Katy, so I can't offer any first-hand experience but I would say it depends on - Where you plan to stay & how flexable you are with that plan: The larger towns will have several motel options. The smaller towns may have only one B&B. Also, some of the larger towns are off of the trail and on the other side of the Missouri river.
The time of year: I believe the B&B's are busiest in late summer and fall. Sedalia has the state fair in (August, I think), Hermann has month-long festivals in May and October, and other towns have weekend festivals during summer and fall.