Bill Gates was in the news, and not in a good way, when he shook hands with the Korean President and created a storm of controversy when he only offered one hand, even worse, his other hand was in his pocket.
See this brief summary of the incident Whenever you meet someone who is either senior in rank or age to yourself you should always do a "two handed" handshake. I remember one of the first things a protocol officer taught me when arriving in Korea was how to shake hands with senior Korean military officers. One technique is to touch your left hand to the inside of your right arm. The gesture is the same and perhaps more comfortable.
Also, if you give anything to another person who is senior to you, use two hands. Watch Asian waitstaff return change to you and you should see them using this technique to show respect (I'm old!).
As our communities become more diverse we need to pay attention to the little things. It can make a huge difference.