I didn't use to AirPlay to my Apple TV from my laptop (MacBook Air) much before, but I've started to more frequently. Got tired of the stuttering and found this thread. I didn't want to disable bluetooth, so I kept trying to figure out a way to make it work.
My scenario is streaming from iTunes only. I'm not doing AirPlay of my whole monitor or of all sounds. I noticed that the stuttering would happen while using other apps, but if I stayed on iTunes, it wouldn't happen. So my solution has been to use the MiniPlayer with the "Keep miniplayer on top of all windows" option selected in the Advanced preferences. It's kind of annoying since I don't actually like the miniplayer, but it has worked at preventing the stuttering so far. Just thought I'd throw it out there for anyone who might stumble on this thread and is in the same scenario that I am.
I'm curious if this is fixed in El Capitan. I plan on upgrading this week, so I'll report back if it fixes things. Or maybe someone on this thread who has already upgraded can comment on that.