You should take a look to popovers methods:

In order to show the popover you need to use:

$('#element').popover('show');

Instead to use:

$('[data-toggle="popover"]')

selector I suggest you to address directly your element.

$('#bulk_actions_btn_new')  or $(this)

If you want to use the data attribute for selecting elements you need to use the filter function.

In order to avoid flickering effects you can show the popover only if it is hidden. If you click too fast on the button you can avoid to hide the popover handling the hide.bs.popover event.

The snippet:

$(document).on('click', '#bulk_actions_btn', function (e) {
    //
    // If popover is visible: do nothing
    //
    if ($(this).prop('popShown') == undefined) {
       $(this).prop('popShown', true).popover('show');
    }
});

$(function () {
    $('#bulk_actions_btn').on('hide.bs.popover', function (e) {
        //
        // on hiding popover stop action
        //
        e.preventDefault();
    });
});

<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://code.jquery.com/jquery-2.1.1.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>



<button type="button" id="bulk_actions_btn"
        class="btn btn-default has-spinner-two"
        data-toggle="popover"
        data-placement="bottom" data-original-title=""
        data-content="Click any question mark icon to get help and tips with specific tasks"
        aria-describedby="popover335446"> Apply
</button>

Just check your condition inside

$(document).ready(function(){
     //Your condition here 
});


    
                

you need to enable popover before it can be used. They are not enabled by default. So when you call popover() method, you are actually initializing the popover. You do that on click event and hence it doesnt work for the first time. You should do that when document.ready is triggered like so -

$(document).ready(function(){
    $('[data-toggle="popover"]').popover();
});

This will enable all bootstrap popovers in your code