Most years there are still some good hotel deals right up until the last minute. But a couple recent years every hotel room in the city sold out. It has more to do with what other events are going on in the city that weekend. One year it was Mardi Gras, and I didn't realize St. Louis has the 2nd largest Mardi Gras celebration for any US city. Every hotel was booked when we tried to get an extra room. And 2 years ago there was some kind of Home Crafting and Quilting convention in the Convertion Center/Dome the same weekend as the MVC Tournament. Believe it or not, home crafts/quilting is one of the most popular hobbies in the country and again every hotel downtown was filled.
It is much better to book early and be sure you have a room rate that allows cancellation. You can then always cancel if you decide not to go, or get a better room deal.
Bradley is staying at the Renaissance Grand, 800 Washington St. for the 5th straight year. I would advise staying at the team hotel because a lot goes on there.
They currently show room availability for $149 a night, and suites for $169 a night (a better deal), but they might still have some of the block rooms set aside for Bradley fans. You would need to call the hotel direct and ask the reservation person at the hotel (not the 800-number reservations) about the room block for the MVC Tournament/Bradley. Be persistent, when I booked these rooms it took them about 4 times to look into their files and find them.
http://www.marriott.com/hotels/travel/stldt-renaissance-st-louis-grand-and-suites-hotel/