Student or Learner
When someone is going for a dring, is it better to ask: Are you going out??? OR Are you leaving????
Are you going out? seems to focus more on what will happen later, once the person has left.
Are you leaving? seems to focus more on the act of leaving and expresses less concern/interest towards what will happen later, once the person has left.
Take for example a student in a classroom who picks up his/her bag in the middle of a lesson and walks toward the door. The teacher would probably say are you leaving? The teacher (at this moment in time) is not so much concerned about where the student is going, but is more concerned with the fact that the person is walking out of the lesson. If the student were to answer yes, then the teacher would probably follow up with where are you going?
To answer your question, are you going out? is the better of the two. In the context of your situation it is essentially a shortened version of are you going out for a drink?
These are not rules, but this is how I would interpret the difference between the questions.
I am not a teacher.