Is there any hotels that have a shuttle to Busch stadium?
SS - it's a 20 minute drive.
Use the Redbird Express. You get this at St Clair Sq. Most hotels are located just across the highway.
The Redbird Express leaves from the mall that is a 2 minute drive from most of the hotels in the area. It is $5/person, round trip and drops you off across the street from the stadium. The busses run continuously starting 2 hours before the game and the last bus leaves the stadium 45 minutes after the game. It's a great deal.