AirPlay YouTube from OS X
You have many ways to do this, but the easiest or simplest way to do this would be to mirror your whole display to the apple TV using the icon in your status bar, if you already have air play mirroring set up. If you don't have it set up go to system preferences > display and there should be an option in your lower left-hand corner. Unlike in iOS, airplay isn't really targeted towards specific apps. I don't really know about the Bose thing, but if you're referring to a sound system, as long as it's hooked up to your TV you should be fine. If you mirror and the sound still plays from your computer try changing the output in system preferences > sound