The answer by Nick Mitchinson is for Bootstrap version 2.
If you are using Bootstrap version 3, then forms have changed a bit. For bootstrap 3, use the following instead:
<div class="form-horizontal">
<div class="form-group">
<div class="col-md-6">
<textarea class="form-control" rows="3" placeholder="What's up?" required></textarea>
</div>
</div>
</div>
Where, col-md-6 will target medium sized devices. You can add col-xs-6 etc to target smaller devices.