The jQuery that you've written will be executed once, when the page loads. If you want some of it to be executed when your drop down changes, then you need to put it in an event handler.
If this doesn't work as expected, you might want to get rid of the sub Dropdownlist1_SelectedTextChanged and have jQuery handle that functionality instead.
//Putting code inside of here assigns it to the 'change' event of #Dropdownlist1
var label = $('#HiddenField1').val();
}).change(); //putting this here fires the 'change' event once, on page load, to initialize things