Bean is an object that follows JavaBeans programming methodology. The simplest bean has private attributes and so-called getters and setters. They are the methods, which get the property and set it. The more complicated bean has also some events and event listeners attached, but they are not used usually in web applications.
So, every attribute, that follows JavaBeans methodology is a bean; and that's why the answer to question "when attributes become beans?" is "when developer developes the attribute classes to be beans".