You have to make a fake drop down menu. Basically you use a "text" input field then use javascript to, onclick, display a div with the other options just below the input field. That div will contain all the stored values from the database and will be hidden till the javascript changes its display value. Then for the values in the div you again use an onclick to capture the value they clicked on and place it in the input field.
To make it look like a normal drop down menu you can make a button with the down arrow that is placed next to the text input field and use the onclick to run the javascript function with it as well. Then for the div you set the height and use the overflow CSS element to have the scroll bar like in a normal drop down menu.
Now that is the simplified break down hopefully it gets you started at least.