As soon as you unlock the Clothing Customizer (by beating Mission 1-1 in Story Mode), you can go there and buy any bear body you want. Some of the bear bodies are expensive, but the ones you were offered at the very beginning of the game are cheap.
The Clothing Customizer is the bottom-right button on the main menu. Bear bodies are located on the last tab in the Clothing Customizer. You'll probably have to scroll the tabs in order to see the one for bear bodies.