overlap notification badge on glyph in Bootstrap 3

Try this:

/* CSS used here will be applied after bootstrap.css */
.badge-notify{
   background:red;
   position:relative;
   top: -20px;
   left: -35px;
}


<div class="container">
  <button class="btn btn-default btn-lg btn-link" style="font-size:36px;">
    <span class="glyphicon glyphicon-comment"></span>
  </button>
  <span class="badge badge-notify">3</span>
</div>

Bootply: http://www.bootply.com/7teIvGLIzY