First, OTC time has nothing to do with making an experience feel personal. Every single client is different, and every provider-client relationship has its own particular 'feel.' Of course we get to know each other, and become more familiar with each other's likes, dislikes, real-life goings-on, etc. The interactions can be genuine even while staying confined to the hours of the appointment.
Personally, I would always rather 'kick back' on my own time, in my sweatpants, on my couch, with my family/friends/boyfriend and civvie activities. When I'm with you, you expect me to look, behave, and treat you a certain way - and that is a service (which can get very tiring).
Just let her leave, and don't drop hints about 'oh, I'm getting a drink at this ritzy place,' or, 'oh, we didn't finish this bottle of wine, have one more glass or it will just go to waste,' or say 'you don't have to leave now, I don't mind if you stay longer.' For every ten clients she sees, nine and a half ask her for OTC time - remember that.
Be even more alert than she is about when her time is up, and just let her go. That courtesy will earn her heartfelt appreciation. If she decides she wants to stay longer, let her bring it up to you, rather than you putting her in an awkward position. And don't expect it to happen every single time