With Bootstrap 3.2 you can wrap each iframe in the responsive-embed wrapper of your choice:
http://getbootstrap.com/components/#responsive-embed
<!-- 16:9 aspect ratio -->
<div class="embed-responsive embed-responsive-16by9">
<iframe class="embed-responsive-item" src="…"></iframe>
</div>
<!-- 4:3 aspect ratio -->
<div class="embed-responsive embed-responsive-4by3">
<iframe class="embed-responsive-item" src="…"></iframe>
</div>
If you don't want to wrap your iframes, you can use FluidVids https://github.com/toddmotto/fluidvids. See demo here: http://toddmotto.com/labs/fluidvids/
<!-- fluidvids.js -->
<script src="js/fluidvids.js"></script>
<script>
fluidvids.init({
selector: ['iframe'],
players: ['www.youtube.com', 'player.vimeo.com']
});
</script>