You can do this with Flexbox and media queries. 
As for flexbox you can just use display: flex and align-items: center on parent element and that will be row in this case. 
Now you just need to adjust min-width in media queries to be same as bootstrap breakpoints So for example if you are using col-sm-6 bootstrap class, then 768px is break point and you will use @media(min-width: 768px) { } in your media queries. 
- For col-sm-you can use@media(min-width: 768px)Fiddle
- For col-md-you can use@media(min-width: 992px)Fiddle
- For col-lg-you can use@media(min-width: 1200px)Fiddle
@media(min-width: 768px) {
  .flex {
    display: flex;
    align-items: center;
  }
}
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet"/>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap-theme.min.css" rel="stylesheet"/>
<div class="container-fluid">
  <div class="row flex">
    <div class="col-sm-6">
      <img src="http://rack.2.mshcdn.com/media/ZgkyMDE1LzA5LzEzLzNjL2dvb2dsZXRodW1iLmIyNGE0LmpwZwpwCXRodW1iCTk1MHg1MzQjCmUJanBn/63126c72/af4/google-thumb.jpg" class="img-responsive" />
    </div>
    <div class="col-sm-6 text-center">
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
    </div>
  </div>
</div>
 
 
Instead of Flexbox you can also get vertical-align with CSS Tables and again you have to adjust your queries with bootstrap breakpoints same as for flexbox. With tables you have to remove float from columns with float: none to get vertical-align.
@media(min-width: 768px) {
  .row.display_table {
    display: table;
  }
  
  .col-sm-6.left_cell, .col-sm-6.right_cell {
    display: table-cell;
    vertical-align: middle;
    float: none;
  }
  
  img {
    width: 100%;
  }
}
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet"/>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap-theme.min.css" rel="stylesheet"/>
<div class="container-fluid">
  <div class="row display_table">
    <div class="col-sm-6 left_cell">
      <img src="http://rack.2.mshcdn.com/media/ZgkyMDE1LzA5LzEzLzNjL2dvb2dsZXRodW1iLmIyNGE0LmpwZwpwCXRodW1iCTk1MHg1MzQjCmUJanBn/63126c72/af4/google-thumb.jpg" class="img-responsive" />
    </div>
    <div class="col-sm-6 right_cell text-center">
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
      <p>This is some text some text some more text</p>
    </div>
  </div>
</div>