It seems that in iOS you cannot use .blur() on a select element, the event will be ignored.
Note: in iOS the user is expected to tap the Done button. Why confuse your end-user by introducing unexpected interaction and behavior (= not provided by the OS to begin with). For example, what if the user selected by mistake? Instead of being able to correct on the spot, s/he will be forced to tap again and select again... I recommend leaving it with the default behavior.
Updated example: instead of removing the select from the DOM and re-introducing it, I've found this.
The below works only in iOS6, though, per the question. It doesn't work in iOS7.
HTML
<div id="mySelectDiv">
    <select id="mySelect">
        <option value="volvo">Volvo</option>
        <option value="saab">Saab</option>
        <option value="mercedes">Mercedes</option>
        <option value="audi">Audi</option>
    </select>
</div>
Selected option: <input type="text" id="selectedOption"/>
JavaScript
function wlCommonInit(){
    $("#mySelect").bind('change', changeValue);
}
function changeValue() {
    var mySelectedIndex = $("#mySelect option:selected").index();
    $("#selectedOption").val($("#mySelect option:selected").text());
    if($("#mySelect").is("select")){
        var fakeSelect = $("#mySelect").clone();
        $("#mySelect").replaceWith(fakeSelect);
        $("#mySelect").bind('change', changeValue);
        $("#mySelect").prop('selectedIndex', mySelectedIndex);
    }
}