In order to produce products in the bakery, you first need to move the necessary items from your storage into the bakery itself. To do this, click on the bakery and choose the truck icon. You'll then see a menu that allows you to move items; you can choose which items and exactly how many you need!

The exceptions to this are the recipes that appear with a red background in the 'Produce' menu; these use resources directly from your main storage. You can start producing these without having to move ingredients first.