You basically have two options: you can use a shuttle service, or take the train (Amtrak).
There are a handful of shuttle services whose business is to simply transport riders and their bikes from point A to point B on the trail. They all serve any point on the trail, so any of them should be willing to take you & your bike from St Charles to Sedalia.
This link will give you a list of all shuttle services
Regarding taking the train, one problem is that you would have to get from trail's end in St Charles to the Amtrak station in Kirkwood, which is about 15-20 miles of street riding. If you're comfortable with street riding in areas where you may not be familiar, then it's no big deal. But some riders are not up for such a challenge, in which case shuttles are the only option.
This entry on our FAQ page discusses
using Amtrak to get to some point on the trail
And here's a page discussing
how to get to the Katy Trail from the Kirkwood Amtrak station
Well, there's always a third option too: make it a round trip and
ride back to Sedalia! Most riders are pretty well worn out by the time they have covered the 190 miles from Sedalia to St Charles, but it's always an option if you have the time and energy. Everything really does look different coming from the other direction. Here's a ride report from a couple who did the
Clinton-to-St Charles-to-Clinton round trip.