A bastard smile is an expression used by people when they have succeeded in annoying you or making you lose your temper. These bastards find it fun to be a nuisance to you and can’t wait for you to react, and when you do they will laugh or pull a bastard smile. The bastard smile can also be used to further irritate people, especially when they are powerless to act, for example, some kids are playing football and a group of adults come along pick up the ball then hold it over their heads and pull a bastard smile.
"you will never believe what happened the other day I got out my car to went pay for my fuel at the petrol station, when I turned around some guy was getting into my car, I ran out to try to stop him but I was to late. when he drove off, he looked at me and pulled a bastard smile."