How does one access and manage the mysql server over the Internet?

How does one access and manage the mysql server over the Internet? -- Linux Enterprise Application-Linux server application information. For details, refer to the following section. I used to use linux and did not manage it. Recently I was eager to learn about linux management. So I mounted two servers in the IDC:
A web Server (A) runs A program (A public IP and A private IP );
Another mysql Server (B) dedicated to database (only one private IP address ).

The two servers are connected through a private IP address.

Question:
1) How can I manage server B through server A? management refers to (the automatic backup implemented by the program will not be mentioned for some configuration of server B or manual backup of important data)
2) If yes, how can this problem be achieved?
3) if not, must B also have a public IP address to implement it?
Please answer! Thank you!