You are absolutely allowed to play with your partner without expectation of others interfering! If the club etiquette is followed, nobody should encroach on you, but if you choose to play in a bigger room on a large bed, expect others to 'share' the bed. If someone wants to join you, they ought to clearly ask. And you are totally in your right to say 'no thank you'.
As for 'finishing' - I'd say the general rule is courtesy. It is likely that others might want to play where you just finished so you ought to keep it as tidy as possible. Plan to bring a towel and be aware of your surroundings. If you're a sloppy shooter, it might be best to keep it in the discharge barrel until your weapon is safe (sorry, military analogy there).