Bow to say hello and goodbye say “ni hao” (你好). To be super polite ask if they have already eaten. If they haven’t then invite them for a meal to make a great impression. Shake hands and bow is both accepted. Bowing in general is a sigh of respect. Many older Chinese lower their eyes during the greeting. This is to show they respect you.
Have you eaten?
After a greeting it’s always polite to ask: Have you eaten? is the direct translation from Chi le ma (吃了吗？), but indeed it is a greeting phrase when people meet each other, representing an intimate relations between them. It’s important to understand this is NOT an invitation for meal.
When meeting a Chinese host avoid to give flowers. Flowers (especially Chrysanthemum) are almost always connected to funerals. So if you like a Chinese woman think twice before you give her some flowers. Flowers are common in a lot of countries but not in China.