I'm not sure about the Market St Bridge, but I know that Coolidge Park has a pavillion available to rent for events. Here is an bit of info from the City of Chattanooga website
The Walker Pavilion, Coolidge Park Carousel and Outdoor Chattanooga Center are popluar venues that can be rented for special events, birthday parties, and programs by calling the City's 311 Central Information System. (423) 425-6311.
And a link to the webpage for all of the info:
Chattanooga is full of beautiful places to hold your wedding. I've made many wedding cakes for Chattanooga venues, so if you need any other recomendations I'm happy to help! Good Luck!
Click on each tool to see a sample.