When I was a TA, I'd have students constantly try to add me on Facebook. The conversation would go nearly exactly like you'd describe:
Are you on Facebook? Is this your profile?
Yes, but I'm not gonna accept your friend request.
The reply was usually a bit snarky with a bit of a chuckle, and that did it for most college-aged people. The few times someone persisted, I explained that Facebook is an aspect of my social life, not my professional life, and I intended to keep it that way.