Your boss has higher status than you for two reasons: he's male and he's Korean. Chances are that he's also older than you. That makes three reasons. So, you must be prepared to show respect to him at all times. More importantly, you must show respect in the Korean way because he might not recognize respect that's paid in a Western manner.
When you bow, don't do the quick little head bobbing thing. You don't need to bend at the waist to make your torso parallel to the ground or anything, but you should bow more than just your head. Also, don't make it quick and jerky. A slow bow shows due respect.
Your boss may or may not try to shake hands with you. Don't worry if your reaction shows that you are uncomfortable with this hand contact. Because you are a woman, he will just think highly of you for showing a feminine reaction.
Don't look into his eyes all the time while he's speaking to you if this makes him uncomfortable.
Never interrupt your boss when he's dealing with parents unless it's extremely important and if you do, be sure to smile at the parents and give a graceful little bow to excuse your rudeness.
Try not to speak so fast that your boss has difficulties in understanding you. When he can't understand what you say, he feels slightly inferior which will make him feel uncomfortable around you.
Do not flirt or act in any way suggestive around your boss.
Never let your boss see you smoking or getting drunk. Generally, men like it when women drink, but don't get drunk around your boss. Keeping a clear head can help prevent misunderstandings.
You can refuse to be alone in a room with your boss when the door is closed. Again, this will make him think more highly of you that you show traditional values.
Try not to argue or contradict your boss in front of other people. Even if the present company knows no English, they can all understand body language and pick up a lot on the tone voice used.
Basically, you should try to appear as professional as possible in all situations. Imagine yourself as a working woman of the 1940s. The only really safe place to cut loose and act silly is if you, your boss, and your co-workers get together in a no-rae-bang (singing room). If you sing, no matter how badly, your boss will love the effort.