A shuttle service will get you where you need to go. These services operate like taxis for the trail, shuttling you and your bikes and gear from one point on the trail to another point on the trail (or beyond). Here is a
list of shuttle services.
I know that at least the two services based in St Charles (TC Tours & Katy Trail Shuttle) will take you between the airport and the St Charles trailhead, for somewhere in the neighborhood of $30. They generally charge by the vanload, so it’s the same price for one passenger as for two.
Any of the shuttles will take you from Clinton to St Charles. I don’t know what they all charge, but you might expect about $250-350. Again, this is per van so it’s not so bad if you can split it with other riders.
Another option for your return trip is to take the Amtrak train back to your starting point. Amtrak stops at Sedalia, which is on the trail but 35 miles from Clinton, so you’ll have to back-track 35 miles from trail’s end to get to the station. The train does not stop in St Charles, but it does stop in Kirkwood, which is in St Louis County. Either of the two St Charles-based shuttles mentioned above will take you from the Kirkwood train station to Lambert St Louis airport, again for something like $30. Here is a web page with
more details on the Amtrak option. Amtrak is a popular option with many trail users.