If you absolutely have to expose mysql to the public network then you should set a very complex password, and consider using iptables to limit those addresses that can access the service remotely.
However as general rule, for whatever reason you want to export MySQL to the network, it is not a good idea. If you are on linux, (or with putty on windows) you can use SSH and a local port forward to make the remote database appear to local development applications with a command like
ssh firstname.lastname@example.org -L 3306:localhost:3306
you can use the
show grants for 'user' command to see which users have access to your database, and which hosts they can connect from. You can also use the following commands (as a starting point) for enumerating the users who can access the server, database locally or remotely;
select user, host, db from mysql.db\G
select Host,Db from mysql.host\G
select user, host from mysql.user\G
you can also use DROP USER
DROP USER 'jeffrey'; to delete the accounts that have been created.