You can't move anything to your bag before you complete a purchase successfully.
Try clearing both your browser & Flash cache first, then restart your browser. If that doesn't help, try another browser to access the ProShop. (Opera didn't work for me in the ProShop, but Chrome did.)
You equip your bag by going to your Profile Page, then click on Equipment and the Edit Equipment button. A pop-up window will open for you where you may drag&drop any club & ball you wish to use in your next round.