Here is the documentation that I believe you are looking for:
http://getbootstrap.com/css/#responsive-utilities-classes
You will want to wrap the content you want to hide / show the desired class.
For example, if you want to hide a section on small (tablets) screens:
<section class="hidden-sm"> <p>This content won't be visible on a tablet, or screen resolution ≥768p and < 992px</p> </section>
And vice versa, if you only want to show something on the tablet:
<section class="visible-sm"> <p>This content will only be visible on a tablet, or screen resolution ≥768px and < 992px</p> </section>
For your button, something like this will only appear on medium and large screens:
<div class="btn btn-primary visible-md visible-lg">Carousel Button</div>
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