How do you handle yourself when you are in a position of power/authority and someone upsets you?

Depending on how serious thet behavior was to challenging your authority and power you could go with D and challenge their behavior in front of the people they've included in the drama. I generally believe that you should praise in public and critisize in private - but some employees don't allow you to behave that way.

So I'd definately let the person know - privately at first that what or how they did or said was unacceptable and cannot continue or there will be consequences.

Always keep your behavior from becoming part of the problem or your authority will only be in name.

It would depend on what the person did. B is usually the best approach, but being upset by something doesn't necessarily mean that it needs to be discussed, so C can be just as valid. Screaming at someone in front of others isn't very professional, but sometimes things boil over and it happens. I've done it--when you have someone questioning your authority and other approaches aren't working, yelling at them won't make much of a difference. They'll either be put in their place, or they'll continue to have a problem with you. Or they'll leave, which can be beneficial.

A) Asshole move, will cause resentment and loss of respect
B) good move
C) passive aggressive and doesn't really solve the problem

Pull them aside.

B) is the most professional way to go.

Pull them aside and discuss what is bothering me and what I expect to happen.

I'm a cop, so that doesn't usually happen. But when it does, they go in cuffs.

Pull them aside, it's the only way. Not even for their sake but for the sake of your own reputation and image in the eyes of the others. A leader can only be a bully in a despotic environment, which a workplace for instance is not.