I use AJAX to do this. You have your partial with your typical twitter modal template html:
<div class="container">
  <!-- Modal -->
  <div class="modal fade" id="LocationNumberModal" role="dialog">
    <div class="modal-dialog">
      <!-- Modal content-->
      <div class="modal-content">
        <div class="modal-header">
          <button type="button" class="close" data-dismiss="modal">
            ×
          </button>
          <h4 class="modal-title">
            Serial Numbers
          </h4>
        </div>
        <div class="modal-body">
          <span id="test"></span>
          <p>Some text in the modal.</p>
        </div>
        <div class="modal-footer">
          <button type="button" class="btn btn-default" data-dismiss="modal">
            Close
          </button>
        </div>
      </div>
    </div>
  </div>
</div>
Then you have your controller method, I use JSON and have a custom class that rendors the view to a string. I do this so I can perform multiple ajax updates on the screen with one ajax call. Reference here: Example but you can use an PartialViewResult/ActionResult on return if you are just doing the one call. I will show it using JSON..
And the JSON Method in Controller:
public JsonResult LocationNumberModal(string partNumber = "")
{
  //Business Layer/DAL to get information
  return Json(new {
      LocationModal = ViewUtility.RenderRazorViewToString(this.ControllerContext, "LocationNumberModal.cshtml", new SomeModelObject())
    },
    JsonRequestBehavior.AllowGet
  );
}
And then, in the view using your modal: You can package the AJAX in your partial and call @{Html.RenderPartial... Or you can have a placeholder with a div:
<div id="LocationNumberModalContainer"></div>
then your ajax:
function LocationNumberModal() {
  var partNumber = "1234";
  var src = '@Url.Action("LocationNumberModal", "Home", new { area = "Part" })'
    + '?partNumber='' + partNumber; 
  $.ajax({
    type: "GET",
    url: src,
    dataType: "json",
    contentType: "application/json; charset=utf-8",
    success: function (data) {
      $("#LocationNumberModalContainer").html(data.LocationModal);
      $('#LocationNumberModal').modal('show');
    }
  });
};
Then the button to your modal:
<button type="button" id="GetLocBtn" class="btn btn-default" onclick="LocationNumberModal()">Get</button>