Here's a simplified version of your markup that helps more easily reproduce the issue:
<div class="row">
<div class="col-xs-2 pull-bottom"
style="height:100px;background:blue">
</div>
<div class="col-xs-8 pull-bottom"
style="height:50px;background:yellow">
</div>
</div>
So how do we vertically align each column to the bottom? See vertical-align with bootstrap 3:
.pull-bottom {
display: inline-block;
vertical-align: bottom;
float: none;
}