WP Media Uploader modal conflicts with Bootstrap modal

Just proxy the modal-open class for Bootstrap like this:

.bs-modal-open {
  overflow: hidden;
}

.bs-modal-open .modal {
  overflow-x: hidden;
  overflow-y: auto;
}

// or using sass …

.bs-modal-open {
  @extend .modal-open;
}

Add/remove the bs-modal-open class to the body when opening/closing a BS modal:

$('.bs-modal')
  .on('show.bs.modal', function (e) {
    $('body').addClass('bs-modal-open');
  })
  .on('hidden.bs.modal', function (e) {
    $('body').removeClass('bs-modal-open');
  });

Finally add the bs-modal class to each of your BS modals:

<div class="modal bs-modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel">
  …
</div>