You can listen to the "close" event of the first model to open the second model:
Bind a function to Twitter Bootstrap Modal Close
$('#my-modal').on('hidden.bs.modal', function () {
  window.alert('hidden event fired!');
})
Manually open the second model:
$('#otherModel').modal('toggle') 
An example:
Your HTML code:
<!-- Button trigger modal -->
<a data-toggle="modal" href="#myModal" class="btn btn-primary btn-lg">Launch demo modal</a>
<!-- Modal -->
<div class="modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
        <h4 class="modal-title">Modal title</h4>
      </div>
      <div class="modal-body">
        ...
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
        <button type="button" class="btn btn-primary">Save changes</button>
      </div>
    </div><!-- /.modal-content -->
  </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
<div class="modal fade" id="myModal2" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
        <h4 class="modal-title">Modal title</h4>
      </div>
      <div class="modal-body">
        ...
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
        <button type="button" class="btn btn-primary">Save changes</button>
      </div>
    </div><!-- /.modal-content -->
  </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
Javascript:
  $('#myModal').on('hidden.bs.modal', function() {
    $('#myModal2').modal("toggle");
  });