A good interuption is also "I'm sorry..." "I'm sorry, I really need to go." And then follow with 'Thank You" because that implies good-bye. I never knew 'Thank You' meant goodbye, until I was a hotel one day. There were some tourists from the country, and they weren't expected to have a man carry their luggage up to their room. They knew they were supposed to give him a tip, but they gave it too soon, when they got to the elevator. The man took the tip and left, and they stood there wondering what to do with their suitcases. They 'thanked him' with the tip too early! It is a delicate social point, but thanking someone 'wraps up' the interaction and brings it to finish. So when you want to end an interaction, 'Thank you' is often a good way to do it.

You can make like if you're sleeping and snore ......Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z........

Just say, 'It's been great talking to you, but I really must go. We'll catch up soon, OK? Bye'

You can break the eye contact and say WELL or AT ANY RATE . but be honest please . you always must be honest . for example : well . i spent a great time with you but i`ve got to do sth else . I`ll get back to ya . Nice meeting you . and then you go away

Respond with a few verbal nods to a few statement then politely interrupt the speaker and say " I am sorry for interrupting but I have to go now..." as simple as that. In that way the speaker will not feel bad & think that you do not want to talk to him/ her.