Placing user login and user menu at the bottom right when this is not supported by the theme
Never directly use the Bootstrap theme, create a subtheme from one of the starterkits inside your theme folder (they have readme files inside the starterkits with more info and relevant links depending on which method you prefer to use), and do all your work in the subtheme. This way you can auto-update the bootstrap theme, without loosing all your customisations.

Next step would be to create your own region (for example Footer right) in the info file of your subtheme:

;;;;;;;;;;;;;;;;;;;;;
;; Regions
;;;;;;;;;;;;;;;;;;;;;

regions[navigation]     = 'Navigation'
regions[header]         = 'Top Bar'
regions[highlighted]    = 'Highlighted'
regions[help]           = 'Help'
regions[content]        = 'Content'
regions[sidebar_first]  = 'Primary'
regions[sidebar_second] = 'Secondary'
regions[footer]         = 'Footer'

regions[footer_right]   = 'Footer right'

regions[page_top]       = 'Page top'
regions[page_bottom]    = 'Page bottom'


Next create the region in your page.tmpl.php file. You should override the one used in the Bootstrap theme, with a duplicate you make in your subtheme: YOUR_SUBTHEME/templates/system/page.tpl.php. (Copy the file you have in YOUR_SUBTHEME/bootstrap/system/page.tpl.php)

Go to the footer section in this page.tpl.php file, it should look somewhat like this:

&lt;?php if (!empty($page['footer'])): ?&gt;
  &lt;footer class="footer &lt;?php print $container_class; ?&gt;"&gt;
   &lt;div class="container"&gt;
    &lt;?php print render($page['footer']); ?&gt;
   &lt;/div&gt;
  &lt;/footer&gt;
&lt;?php endif; ?&gt;


And add your new region where you would like it to go (for instance like this), and use the Bootstrap markup to align your content to the right:

&lt;?php if (!empty($page['footer'])): ?&gt;
  &lt;footer class="footer &lt;?php print $container_class; ?&gt;"&gt;

   &lt;?php if (!empty($page['footer_right'])): ?&gt;
    &lt;div class="container"&gt;
     &lt;div class="col-xs-6 col-xs-offset-6 col-sm-4 col-sm-offset-8"&gt;
      &lt;?php print render($page['footer_right']); ?&gt;
     &lt;/div&gt;
    &lt;/div&gt;
   &lt;?php endif; ?&gt;

   &lt;div class="container"&gt;
    &lt;?php print render($page['footer']); ?&gt;
   &lt;/div&gt;
  &lt;/footer&gt;
&lt;?php endif; ?&gt;


Make sure to clear your sites cache when you're doing changes to template files like these. If all is fine, your new region should appear in "structure > blocks", and you should be able to add your login blocks to it.