Is there a shuttle service

Yes.

Not when I went in June. I called the hotel because other Embassy Suites that I have been to have shuttle service, but not the one in St. Charles, Missouri. We took a taxi from the airport to the hotel. When I was at the hotel, I saw that they have shuttle buses but none moved from the parking spot. Call the Embassy Suites that you are traveling to to ask them. In Atlanta when I went many years ago, they have a shuttle.