In terms of paying the bill, it is not unusual to grab the bill and pay for it before your host takes any actions. A-A is very rare in China especially when you are doing business with clients. Even when you are the client, you can do it just to show friendliness.
The Chinese will never let you pay the bill if you don’t insist on it. You might just pay the bill really fast, or even sneak to the cashier and pay secretly before the meal ends. Don’t find it strange when people fight and rush and shout in order to have the privilege to pay the bill. This is the Chinese way to show hospitality, friendship, and generosity. If you lose the opportunity to pay the bill, make sure to express some reluctance and frustration. And don’t forget to show your appreciation to the person who has the honor.
If you are invited to a dinner, chances are that the host is prepared to pay the bill for all the attendants. So don`t rush to go Dutch with him. This is rather annoying because the host may think that you are looking down upon him. However, make sure you have some money in your purse. It will lead to embarrassment if the host wants to go Dutch but you don`t have money to pay for it.
Try not to share the bill while eating together, its a sign of respect to let someone pay the bill. This is no problem as long as you will do it yourself the next time you will have a meal with this person. For Chinese it is still very common to do this when you are going out for a meal with your boss or someone important.