I have never used bootstrap before, but I have done responsive embedding using this iframe technique before – http://webdesignerwall.com/tutorials/css-elastic-videos
Feel free to clean it up a bit, etc. (e.g. aspectRatio should probably be a var to centralize that calculation, etc.).
The downside is that on window resize it has to call that event handler to resize the player, which is kind of hacky and inefficient, but until Longtail implements the responsive design stuff I've been badgering them about (6.4 they say), it's the best way I found to handle this without extensive source code changes.