If you add the SELECT after in javascript you can achieve this:

<select id="mySelect" OnChange="window.location.href=this.value">
    <option>Tagged Stuff and Navigation</option>
</select>

<script>
    if (window.location.href.substring(0,9) === "http://ww") {
    var home_var = "bing.com";    
    }
    else if (window.location.href.substring(0,9) === "https://p") {
    var home_var = "https://px.multiscreensite.com/index.php?url=bing.com";
    }
    else {
    var home_var = "1";
    }
    var select= document.getElementById("mySelect");
    var option = document.createElement("option");
    option.text = "Hope Page";
    option.value = home_var;
    select.add(option);
    console.log(home_var);
</script>

JS Fiddle https://jsfiddle.net/emfvyhq2/