Now, about your code. As I see it, you create your student combo box when you need it. You set its bounds but you don't add it to any control. Perhaps that is in the calling method. Either way, the setBounds is not encouraged; you should use a proper layout manager which will set the bounds for you.
Anyway, getting back to your code. You add an action listener that will retrieve another student (which one?) which you then add. Is this really what you want? Wouldn't you want to load all students from the database immediately and store those in your combo box? A combo box can store any object; it will use the result of toString() by default to display it but you can override this by using your own ListCellRenderer.